初二数学求难题，越难越好！ 八年级下册数学难题,越多越好急!谢谢!!
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17\u3001\uff08\u672c\u98984\u5206\uff09\u7528\u6c7d\u8239\u62d6\u8f7d\u91cd\u91cf\u76f8\u7b49\u6ee1\u8f7d\u8d27\u7269\u7684\u5c0f\u8239\u82e5\u5e72\u53ea,\u5728\u4e24\u6e2f\u4e4b\u95f4\u6765\u56de\u9001\u8d27\u7269.\u5df2\u77e5\u6bcf\u6b21\u62d64\u53ea\u5c0f\u8239,\u4e00\u65e5\u80fd\u6765\u56de16\u6b21;\u6bcf\u6b21\u62d67\u53ea\u5c0f\u8239,\u4e00\u65e5\u80fd\u6765\u56de10\u6b21.\u6bcf\u65e5\u6765\u56de\u6b21\u6570\u662f\u62d6\u5c0f\u8239\u53ea\u6570\u7684\u4e00\u6b21\u51fd\u6570(\u4e00\u5929\u4e2d\u6bcf\u6b21\u62d6\u5c0f\u8239\u53ea\u6570\u4e0d\u53d8).\u95ee\u6bcf\u65e5\u6765\u56de\u591a\u5c11\u6b21,\u6bcf\u6b21\u62d6\u591a\u5c11\u53ea\u5c0f\u8239,\u624d\u80fd\u4f7f\u8fd0\u8d27\u95ee\u9898\u8fbe\u5230\u6700\u5927?
18\u3001\uff08\u672c\u98986\u5206\uff09\u5728\u7b49\u8170 \u4e2d\uff0c \uff0cCD\u5e73\u5206 \u4ea4AB\u4e8e\u70b9D\uff0c\u82e5 \uff0c
\u2460\uff084\u5206\uff09\u6c42 \uff1b
\u2461\uff082\u5206\uff09\u6c42\u8bc1\uff1a \u3002
19\u3001\uff08\u672c\u98986\u5206\uff09\u7ed9\u51fa\u53cd\u6bd4\u4f8b\u51fd\u6570 \u4e0e\u4e00\u6b21\u51fd\u6570 \uff0c\u56de\u7b54\u4e0b\u5217\u95ee\u9898\uff1a
I\u3001\u5f53 \u65f6\uff0c
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II\u3001\u5f53 \u65f6\uff0c
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\u5206\u5f0f\uff1a
\u4e00\uff1a\u5982\u679cabc=1,\u6c42\u8bc1 + + =1
\u89e3\uff1a\u539f\u5f0f= + +
= + +
=
=1
\u4e8c\uff1a\u5df2\u77e5 + = \uff0c\u5219 + \u7b49\u4e8e\u591a\u5c11\uff1f
\u89e3\uff1a + =
=
2( ) =9
2 +4 +2 =9
2\uff08 \uff09=5
=
+ =
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1
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A
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\u7b54\u6848\uff1ar=1
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(2)\u6c42\u76f4\u7ebfAB\u7684\u51fd\u6570\u89e3\u6790\u5f0f\uff1b
\u52fe\u80a1\u5b9a\u7406\uff1a
\u4e00\uff1a\u6e05\u671d\u5eb7\u7199\u7687\u5e1d\u662f\u6211\u56fd\u5386\u53f2\u4e0a\u5bf9\u6570\u5b66\u5f88\u6709\u5174\u8da3\u7684\u5e1d\u738b\uff0e\u8fd1\u65e5\uff0c\u897f\u5b89\u53d1\u73b0\u4e86\u4ed6\u7684\u6570\u5b66\u4e13\u8457\uff0c\u5176\u4e2d\u6709\u4e00\u6587\u300a\u79ef\u6c42\u52fe\u80a1\u6cd5\u300b\uff0c\u5b83\u5bf9\u201c\u4e09\u8fb9\u957f\u4e3a3\u30014\u30015\u7684\u6574\u6570\u500d\u7684\u76f4\u89d2\u4e09\u89d2\u5f62\uff0c\u5df2\u77e5\u9762\u79ef\u6c42\u8fb9\u957f\u201d\u8fd9\u4e00\u95ee\u9898\u63d0\u51fa\u4e86\u89e3\u6cd5\uff1a\u201c\u82e5\u6240\u8bbe\u8005\u4e3a\u79ef\u6570\uff08\u9762\u79ef\uff09\uff0c\u4ee5\u79ef\u7387\u516d\u9664\u4e4b\uff0c\u5e73\u65b9\u5f00\u4e4b\u5f97\u6570\uff0c\u518d\u4ee5\u52fe\u80a1\u5f26\u5404\u7387\u4e58\u4e4b\uff0c\u5373\u5f97\u52fe\u80a1\u5f26\u4e4b\u6570\u201d\uff0e\u7528\u73b0\u5728\u7684\u6570\u5b66\u8bed\u8a00\u8868\u8ff0\u662f\uff1a\u201c\u82e5\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u4e09\u8fb9\u957f\u5206\u522b\u4e3a3\u30014\u30015\u7684\u6574\u6570\u500d\uff0c\u8bbe\u5176\u9762\u79ef\u4e3aS\uff0c\u5219\u7b2c\u4e00\u6b65\uff1a \uff1dm\uff1b\u7b2c\u4e8c\u6b65\uff1a =k\uff1b\u7b2c\u4e09\u6b65\uff1a\u5206\u522b\u75283\u30014\u30015\u4e58\u4ee5k\uff0c\u5f97\u4e09\u8fb9\u957f\u201d\uff0e
\uff081\uff09\u5f53\u9762\u79efS\u7b49\u4e8e150\u65f6\uff0c\u8bf7\u7528\u5eb7\u7199\u7684\u201c\u79ef\u6c42\u52fe\u80a1\u6cd5\u201d\u6c42\u51fa\u8fd9\u4e2a\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u4e09\u8fb9\u957f\uff1b
\uff082\uff09\u4f60\u80fd\u8bc1\u660e\u201c\u79ef\u6c42\u52fe\u80a1\u6cd5\u201d\u7684\u6b63\u786e\u6027\u5417\uff1f\u8bf7\u5199\u51fa\u8bc1\u660e\u8fc7\u7a0b\uff0e
\u89e3\uff1a\uff081\uff09\u5f53S=150\u65f6\uff0ck= = =5\uff0c
\u6240\u4ee5\u4e09\u8fb9\u957f\u5206\u522b\u4e3a\uff1a3\u00d75=15\uff0c4\u00d75=20\uff0c5\u00d75=25\uff1b
\uff082\uff09\u8bc1\u660e\uff1a\u4e09\u8fb9\u4e3a3\u30014\u30015\u7684\u6574\u6570\u500d\uff0c
\u8bbe\u4e3ak\u500d\uff0c\u5219\u4e09\u8fb9\u4e3a3k\uff0c4k\uff0c5k\uff0c
\u800c\u4e09\u89d2\u5f62\u4e3a\u76f4\u89d2\u4e09\u89d2\u5f62\u4e143k\u30014k\u4e3a\u76f4\u89d2\u8fb9\uff0e
\u5176\u9762\u79efS= \uff083k\uff09\u00b7\uff084k\uff09=6k2\uff0c
\u6240\u4ee5k2= \uff0ck= \uff08\u53d6\u6b63\u503c\uff09\uff0c
\u5373\u5c06\u9762\u79ef\u9664\u4ee56\uff0c\u7136\u540e\u5f00\u65b9\uff0c\u5373\u53ef\u5f97\u5230\u500d\u6570\uff0e
\u4e8c\uff1a\u4e00\u5f20\u7b49\u8170\u4e09\u89d2\u5f62\u7eb8\u7247\uff0c\u5e95\u8fb9\u957fl5cm\uff0c\u5e95\u8fb9\u4e0a\u7684\u9ad8\u957f22\uff0e5cm\uff0e\u73b0\u6cbf\u5e95\u8fb9\u4f9d\u6b21\u4ece\u4e0b\u5f80\u4e0a\u88c1\u526a\u5bbd\u5ea6\u5747\u4e3a3cm\u7684\u77e9\u5f62\u7eb8\u6761\uff0c\u5982\u56fe\u6240\u793a\uff0e\u5df2\u77e5\u526a\u5f97\u7684\u7eb8\u6761\u4e2d\u6709\u4e00\u5f20\u662f\u6b63\u65b9\u5f62\uff0c\u5219\u8fd9\u5f20\u6b63\u65b9\u5f62\u7eb8\u6761\u662f( )
A\uff0e\u7b2c4\u5f20 B\uff0e\u7b2c5\u5f20 C\uff0e\u7b2c6\u5f20 D\uff0e\u7b2c7\u5f20
\u7b54\u6848\uff1aC
\u4e09\uff1a\u5982\u56fe\uff0c\u7532\u3001\u4e59\u4e24\u697c\u76f8\u8ddd20\u7c73\uff0c\u7532\u697c\u9ad820\u7c73\uff0c\u5c0f\u660e\u7ad9\u5728\u8ddd\u7532\u697c10\u7c73\u7684 \u5904\u76ee\u6d4b\u5f97\u70b9 \u4e0e\u7532\u3001\u4e59\u697c\u9876 \u521a\u597d\u5728\u540c\u4e00\u76f4\u7ebf\u4e0a\uff0c\u4e14A\u4e0eB\u76f8\u8ddd \u7c73\uff0c\u82e5\u5c0f\u660e\u7684\u8eab\u9ad8\u5ffd\u7565\u4e0d\u8ba1\uff0c\u5219\u4e59\u697c\u7684\u9ad8\u5ea6\u662f \u7c73\uff0e
20\u7c73
\u4e59
C
B
A
\u7532
10\u7c73
\uff1f\u7c73
20\u7c73
\u7b54\u6848\uff1a40\u7c73
\u56db\uff1a\u6069\u65bd\u5dde\u81ea\u7136\u98ce\u5149\u65e0\u9650\uff0c\u7279\u522b\u662f\u4ee5\u201c\u96c4\u3001\u5947\u3001\u79c0\u3001\u5e7d\u3001\u9669\u201d\u8457\u79f0\u4e8e\u4e16\uff0e\u8457\u540d\u7684\u6069\u65bd\u5927\u5ce1\u8c37 \u548c\u4e16\u754c\u7ea7\u81ea\u7136\u4fdd\u62a4\u533a\u661f\u6597\u5c71 \u4f4d\u4e8e\u7b14\u76f4\u7684\u6caa\u6e1d\u9ad8\u901f\u516c\u8def \u540c\u4fa7\uff0c \u3001 \u5230\u76f4\u7ebf \u7684\u8ddd\u79bb\u5206\u522b\u4e3a \u548c \uff0c\u8981\u5728\u6caa\u6e1d\u9ad8\u901f\u516c\u8def\u65c1\u4fee\u5efa\u4e00\u670d\u52a1\u533a \uff0c\u5411 \u3001 \u4e24\u666f\u533a\u8fd0\u9001\u6e38\u5ba2\uff0e\u5c0f\u6c11\u8bbe\u8ba1\u4e86\u4e24\u79cd\u65b9\u6848\uff0c\u56fe\uff081\uff09\u662f\u65b9\u6848\u4e00\u7684\u793a\u610f\u56fe\uff08 \u4e0e\u76f4\u7ebf \u5782\u76f4\uff0c\u5782\u8db3\u4e3a \uff09\uff0c \u5230 \u3001 \u7684\u8ddd\u79bb\u4e4b\u548c \uff0c\u56fe\uff082\uff09\u662f\u65b9\u6848\u4e8c\u7684\u793a\u610f\u56fe\uff08\u70b9 \u5173\u4e8e\u76f4\u7ebf \u7684\u5bf9\u79f0\u70b9\u662f \uff0c\u8fde\u63a5 \u4ea4\u76f4\u7ebf \u4e8e\u70b9 \uff09\uff0c \u5230 \u3001 \u7684\u8ddd\u79bb\u4e4b\u548c \uff0e
\uff081\uff09\u6c42 \u3001 \uff0c\u5e76\u6bd4\u8f83\u5b83\u4eec\u7684\u5927\u5c0f\uff1b
\uff082\uff09\u8bf7\u4f60\u8bf4\u660e \u7684\u503c\u4e3a\u6700\u5c0f\uff1b
\uff083\uff09\u62df\u5efa\u7684\u6069\u65bd\u5230\u5f20\u5bb6\u754c\u9ad8\u901f\u516c\u8def \u4e0e\u6caa\u6e1d\u9ad8\u901f\u516c\u8def\u5782\u76f4\uff0c\u5efa\u7acb\u5982\u56fe\uff083\uff09\u6240\u793a\u7684\u76f4\u89d2\u5750\u6807\u7cfb\uff0c \u5230\u76f4\u7ebf \u7684\u8ddd\u79bb\u4e3a \uff0c\u8bf7\u4f60\u5728 \u65c1\u548c \u65c1\u5404\u4fee\u5efa\u4e00\u670d\u52a1\u533a \u3001 \uff0c\u4f7f \u3001 \u3001 \u3001 \u7ec4\u6210\u7684\u56db\u8fb9\u5f62\u7684\u5468\u957f\u6700\u5c0f\uff0e\u5e76\u6c42\u51fa\u8fd9\u4e2a\u6700\u5c0f\u503c\uff0e
B
A
P
X
\u56fe\uff081\uff09
Y
X
B
A
Q
P
O
\u56fe\uff083\uff09
B
A
P
X
\u56fe\uff082\uff09
\u89e3:\u2474\u56fe10\uff081\uff09\u4e2d\u8fc7B\u4f5cBC\u22a5AP,\u5782\u8db3\u4e3aC,\u5219PC\uff1d40,\u53c8AP\uff1d10,
\u2234AC\uff1d30
\u5728Rt\u25b3ABC \u4e2d\uff0cAB\uff1d50 AC\uff1d30 \u2234BC\uff1d40
\u2234 BP\uff1d
S1\uff1d
\u2475\u56fe10\uff082\uff09\u4e2d\uff0c\u8fc7B\u4f5cBC\u22a5AA\u2032\u5782\u8db3\u4e3aC\uff0c\u5219A\u2032C\uff1d50\uff0c
\u53c8BC\uff1d40
\u2234BA'\uff1d
\u7531\u8f74\u5bf9\u79f0\u77e5\uff1aPA\uff1dPA'
\u2234S2\uff1dBA'\uff1d
\u2234 \ufe65
(2)\u5982 \u56fe10\uff082\uff09\uff0c\u5728\u516c\u8def\u4e0a\u4efb\u627e\u4e00\u70b9M,\u8fde\u63a5MA,MB,MA'\uff0c\u7531\u8f74\u5bf9\u79f0\u77e5MA\uff1dMA'
\u2234MB+MA\uff1dMB+MA'\ufe65A'B
\u2234S2\uff1dBA'\u4e3a\u6700\u5c0f
\uff083\uff09\u8fc7A\u4f5c\u5173\u4e8eX\u8f74\u7684\u5bf9\u79f0\u70b9A', \u8fc7B\u4f5c\u5173\u4e8eY\u8f74\u7684\u5bf9\u79f0\u70b9B'\uff0c
\u8fde\u63a5A'B',\u4ea4X\u8f74\u4e8e\u70b9P, \u4ea4Y\u8f74\u4e8e\u70b9Q,\u5219P,Q\u5373\u4e3a\u6240\u6c42
\u8fc7A'\u3001 B'\u5206\u522b\u4f5cX\u8f74\u3001Y\u8f74\u7684\u5e73\u884c\u7ebf\u4ea4\u4e8e\u70b9G,
A'B'\uff1d
\u2234\u6240\u6c42\u56db\u8fb9\u5f62\u7684\u5468\u957f\u4e3a
D
C
E
B
G
A
F
\u4e94\uff1a\u5df2\u77e5\uff1a\u5982\u56fe\uff0c\u5728\u76f4\u89d2\u68af\u5f62ABCD\u4e2d\uff0cAD\u2225BC\uff0c\u2220ABC\uff1d90\u00b0\uff0cDE\u22a5AC\u4e8e\u70b9F\uff0c\u4ea4BC\u4e8e\u70b9G\uff0c\u4ea4AB\u7684\u5ef6\u957f\u7ebf\u4e8e\u70b9E\uff0c\u4e14 \uff0e
\uff081\uff09\u6c42\u8bc1\uff1a \uff1b
\uff082\uff09\u82e5 \uff0c\u6c42AB\u7684\u957f\uff0e
\u89e3\uff1a\uff081\uff09\u8bc1\u660e\uff1a \u4e8e\u70b9 \uff0c
D
C
E
B
G
A
F
\uff0e
\uff0c
\uff0e
\u8fde\u63a5 \uff0c
AG\uff1dAG,AB\uff1dAF\uff0c
\uff0e
\uff0e
\uff082\uff09\u89e3\uff1a\u2235AD\uff1dDC,DF\u22a5AC\uff0c
\uff0e
\uff0e
\uff0c
\uff0e
\uff0e
\u56db\u8fb9\u5f62\uff1a
\u4e00\uff1a\u5982\u56fe\uff0c\u25b3ACD\u3001\u25b3ABE\u3001\u25b3BCF\u5747\u4e3a\u76f4\u7ebfBC\u540c\u4fa7\u7684\u7b49\u8fb9\u4e09\u89d2\u5f62.
(1) \u5f53AB\u2260AC\u65f6\uff0c\u8bc1\u660e\u56db\u8fb9\u5f62ADFE\u4e3a\u5e73\u884c\u56db\u8fb9\u5f62\uff1b
E
F
D
A
B
C
(2) \u5f53AB = AC\u65f6\uff0c\u987a\u6b21\u8fde\u7ed3A\u3001D\u3001F\u3001E\u56db\u70b9\u6240\u6784\u6210\u7684\u56fe\u5f62\u6709\u54ea\u51e0\u7c7b\uff1f\u76f4\u63a5\u5199\u51fa\u6784\u6210\u56fe\u5f62\u7684\u7c7b\u578b\u548c\u76f8\u5e94\u7684\u6761\u4ef6.
\u89e3\uff1a(1) \u2235\u25b3ABE\u3001\u25b3BCF\u4e3a\u7b49\u8fb9\u4e09\u89d2\u5f62\uff0c
\u2234AB = BE = AE\uff0cBC = CF = FB\uff0c\u2220ABE = \u2220CBF = 60\u00b0.
\u2234\u2220FBE = \u2220CBA.
\u2234\u25b3FBE \u224c\u25b3CBA.
\u2234EF = AC.
\u53c8\u2235\u25b3ADC\u4e3a\u7b49\u8fb9\u4e09\u89d2\u5f62\uff0c
\u2234CD = AD = AC.
\u2234EF = AD.
\u540c\u7406\u53ef\u5f97AE = DF.
\u2234\u56db\u8fb9\u5f62AEFD\u662f\u5e73\u884c\u56db\u8fb9\u5f62.
(2) \u6784\u6210\u7684\u56fe\u5f62\u6709\u4e24\u7c7b\uff0c\u4e00\u7c7b\u662f\u83f1\u5f62\uff0c\u4e00\u7c7b\u662f\u7ebf\u6bb5.
\u5f53\u56fe\u5f62\u4e3a\u83f1\u5f62\u65f6\uff0c\u2220 BAC\u226060\u00b0\uff08\u6216A\u4e0eF\u4e0d\u91cd\u5408\u3001\u25b3ABC\u4e0d\u4e3a\u6b63\u4e09\u89d2\u5f62\uff09
\u5f53\u56fe\u5f62\u4e3a\u7ebf\u6bb5\u65f6\uff0c\u2220BAC = 60\u00b0\uff08\u6216A\u4e0eF\u91cd\u5408\u3001\u25b3ABC\u4e3a\u6b63\u4e09\u89d2\u5f62\uff09.
\u4e8c\uff1a\u5982\u56fe\uff0c\u5df2\u77e5\u25b3ABC\u662f\u7b49\u8fb9\u4e09\u89d2\u5f62\uff0cD\u3001E\u5206\u522b\u5728\u8fb9BC\u3001AC\u4e0a\uff0c\u4e14CD=CE\uff0c\u8fde\u7ed3DE\u5e76\u5ef6\u957f\u81f3\u70b9F\uff0c\u4f7fEF=AE\uff0c\u8fde\u7ed3AF\u3001BE\u548cCF\u3002
\uff081\uff09\u8bf7\u5728\u56fe\u4e2d\u627e\u51fa\u4e00\u5bf9\u5168\u7b49\u4e09\u89d2\u5f62\uff0c\u7528\u7b26\u53f7\u201c\u224c\u201d\u8868\u793a\uff0c\u5e76\u52a0\u4ee5\u8bc1\u660e\u3002
\uff082\uff09\u5224\u65ad\u56db\u8fb9\u5f62ABDF\u662f\u600e\u6837\u7684\u56db\u8fb9\u5f62\uff0c\u5e76\u8bf4\u660e\u7406\u7531\u3002
\uff083\uff09\u82e5AB=6\uff0cBD=2DC\uff0c\u6c42\u56db\u8fb9\u5f62ABEF\u7684\u9762\u79ef\u3002
\u89e3\uff1a\uff081\uff09\uff08\u9009\u8bc1\u4e00\uff09
\uff08\u9009\u8bc1\u4e8c\uff09
\u8bc1\u660e\uff1a
\uff08\u9009\u8bc1\u4e09\uff09
\u8bc1\u660e\uff1a
\uff082\uff09\u56db\u8fb9\u5f62ABDF\u662f\u5e73\u884c\u56db\u8fb9\u5f62\u3002
\u7531\uff081\uff09\u77e5\uff0c \u3001 \u3001 \u90fd\u662f\u7b49\u8fb9\u4e09\u89d2\u5f62\u3002
\uff083\uff09\u7531\uff082\uff09\u77e5\uff0c\uff09\u56db\u8fb9\u5f62ABDF\u662f\u5e73\u884c\u56db\u8fb9\u5f62\u3002
\u4e09\uff1a\u5982\u56fe\uff0c\u5728\u25b3ABC\u4e2d\uff0c\u2220A\u3001\u2220B\u7684\u5e73\u5206\u7ebf\u4ea4\u4e8e\u70b9D\uff0cDE\u2225AC\u4ea4BC\u4e8e\u70b9E\uff0cDF\u2225BC\u4ea4AC\u4e8e\u70b9F\uff0e
\uff081\uff09\u70b9D\u662f\u25b3ABC\u7684________\u5fc3\uff1b
\uff082\uff09\u6c42\u8bc1\uff1a\u56db\u8fb9\u5f62DECF\u4e3a\u83f1\u5f62\uff0e
\u89e3\uff1a(1) \u5185.
(2) \u8bc1\u6cd5\u4e00\uff1a\u8fde\u63a5CD\uff0c
\u2235 DE\u2225AC\uff0cDF\u2225BC\uff0c
\u56fe7
\u2234 \u56db\u8fb9\u5f62DECF\u4e3a\u5e73\u884c\u56db\u8fb9\u5f62\uff0c
\u53c8\u2235 \u70b9D\u662f\u25b3ABC\u7684\u5185\u5fc3\uff0c
\u2234 CD\u5e73\u5206\u2220ACB\uff0c\u5373\u2220FCD\uff1d\u2220ECD\uff0c
\u53c8\u2220FDC\uff1d\u2220ECD\uff0c\u2234 \u2220FCD\uff1d\u2220FDC
\u2234 FC\uff1dFD\uff0c
\u2234 \u25a1DECF\u4e3a\u83f1\u5f62\uff0e
\u8bc1\u6cd5\u4e8c\uff1a
\u8fc7D\u5206\u522b\u4f5cDG\u22a5AB\u4e8eG\uff0cDH\u22a5BC\u4e8eH\uff0cDI\u22a5AC\u4e8eI\uff0e
\u2235AD\u3001BD\u5206\u522b\u5e73\u5206\u2220CAB\u3001\u2220ABC\uff0c
\u2234DI=DG\uff0c
DG=DH\uff0e
\u2234DH=DI\uff0e
\u2235DE\u2225AC\uff0cDF\u2225BC\uff0c
\u2234\u56db\u8fb9\u5f62DECF\u4e3a\u5e73\u884c\u56db\u8fb9\u5f62\uff0c
\u2234S\u25a1DECF=CE\u00b7DH =CF\u00b7DI\uff0c
\u2234CE=CF\uff0e
\u2234\u25a1DECF\u4e3a\u83f1\u5f62\uff0e
\u56db\uff1a\u5728\u77e9\u5f62ABCD\u4e2d\uff0c\u70b9E\u662fAD\u8fb9\u4e0a\u4e00\u70b9\uff0c\u8fde\u63a5BE\uff0c\u4e14\u2220ABE\uff1d30\u00b0\uff0cBE\uff1dDE\uff0c\u8fde\u63a5BD\uff0e\u70b9P\u4ece\u70b9E\u51fa\u53d1\u6cbf\u5c04\u7ebfED\u8fd0\u52a8\uff0c\u8fc7\u70b9P\u4f5cPQ\u2225BD\u4ea4\u76f4\u7ebfBE\u4e8e\u70b9Q\uff0e
(1) \u5f53\u70b9P\u5728\u7ebf\u6bb5ED\u4e0a\u65f6\uff08\u5982\u56fe1\uff09\uff0c\u6c42\u8bc1\uff1aBE\uff1dPD\uff0b PQ\uff1b
\uff082\uff09\u82e5 BC\uff1d6\uff0c\u8bbePQ\u957f\u4e3ax\uff0c\u4ee5P\u3001Q\u3001D\u4e09\u70b9\u4e3a\u9876\u70b9\u6240\u6784\u6210\u7684\u4e09\u89d2\u5f62\u9762\u79ef\u4e3ay\uff0c\u6c42y\u4e0e x\u7684\u51fd\u6570\u5173\u7cfb\u5f0f\uff08\u4e0d\u8981\u6c42\u5199\u51fa\u81ea\u53d8\u91cfx\u7684\u53d6\u503c\u8303\u56f4\uff09\uff1b
\uff083\uff09\u5728\u2461\u7684\u6761\u4ef6\u4e0b\uff0c\u5f53\u70b9P\u8fd0\u52a8\u5230\u7ebf\u6bb5ED\u7684\u4e2d\u70b9\u65f6\uff0c\u8fde\u63a5QC\uff0c\u8fc7\u70b9P\u4f5cPF\u22a5QC\uff0c\u5782\u8db3\u4e3aF\uff0cPF\u4ea4\u5bf9\u89d2\u7ebfBD\u4e8e\u70b9G\uff08\u5982\u56fe2\uff09\uff0c\u6c42\u7ebf\u6bb5PG\u7684\u957f\u3002
\u89e3\uff1a\uff081\uff09\u8bc1\u660e\uff1a\u2235\u2220A=90\u00b0 \u2220ABE=30\u00b0 \u2220AEB=60\u00b0
\u2235EB=ED \u2234\u2220EBD=\u2220EDB=30\u00b0
\u2235PQ\u2225BD \u2234\u2220EQP=\u2220EBD \u2220EPQ=\u2220EDB
\u2234\u2220EPQ=\u2220EQP=30\u00b0 \u2234EQ=EP
\u8fc7\u70b9E\u4f5cEM\u22a5OP\u5782\u8db3\u4e3aM \u2234PQ=2PM
\u2235\u2220EPM=30\u00b0\u2234PM= PE \u2234PE= PQ
\u2235BE=DE=PD+PE \u2234BE=PD+ PQ
\uff082\uff09\u89e3\uff1a\u7531\u9898\u610f\u77e5AE= BE \u2234DE=BE=2AE
\u2235AD=BC=6 \u2234AE=2 DE=BE=4
\u5f53\u70b9P\u5728\u7ebf\u6bb5ED\u4e0a\u65f6\uff08\u5982\u56fe1\uff09
\u8fc7\u70b9Q\u505aQH\u22a5AD\u4e8e\u70b9H QH= PQ= x
\u7531\uff081\uff09\u5f97PD=BE- PQ=4- x
\u2234y= PD\u00b7QH=
\u5f53\u70b9P\u5728\u7ebf\u6bb5ED\u7684\u5ef6\u957f\u7ebf\u4e0a\u65f6\uff08\u5982\u56fe2\uff09\u8fc7\u70b9Q\u4f5cQH\u22a5DA\u4ea4DA\u5ef6\u957f\u7ebf\u4e8e\u70b9H\u2019 \u2234QH\u2019= x
\u8fc7\u70b9E\u4f5cEM\u2019\u22a5PQ\u4e8e\u70b9M\u2019 \u540c\u7406\u53ef\u5f97EP=EQ= PQ \u2234BE= PQ-PD
\u2234PD= x-4 y= PD\u00b7QH\u2019=
\uff083\uff09\u89e3\uff1a\u8fde\u63a5PC\u4ea4BD\u4e8e\u70b9N\uff08\u5982\u56fe3\uff09\u2235\u70b9P\u662f\u7ebf\u6bb5ED\u4e2d\u70b9
\u2234EP=PD=2 \u2234PQ= \u2235DC=AB=AE\u00b7tan60\u00b0=
\u2234PC= =4 \u2234cos\u2220DPC= = \u2234\u2220DPC=60\u00b0
\u2234\u2220QPC=180\u00b0-\u2220EPQ-\u2220DPC=90\u00b0
\u2235PQ\u2225BD \u2234\u2220PND=\u2220QPC=90\u00b0 \u2234PN= PD=1
QC= = \u2235\u2220PGN=90\u00b0-\u2220FPC \u2220PCF=90\u00b0-\u2220FPC
\u2234\u2220PCN=\u2220PCF\u2026\u2026\u2026\u2026\u20261\u5206 \u2235\u2220PNG=\u2220QPC=90\u00b0 \u2234\u25b3PNG\uff5e\u25b3QPC
\u2234 \u2234PG= =
\u4e94\uff1a\u5982\u56fe,\u8fd9\u662f\u4e00\u5f20\u7b49\u8170\u68af\u5f62\u7eb8\u7247,\u5b83\u7684\u4e0a\u5e95\u957f\u4e3a2,\u4e0b\u5e95\u957f\u4e3a4,\u8170\u957f\u4e3a2,\u8fd9\u6837\u7684\u7eb8\u7247\u5171\u67095\u5f20.\u6253\u7b97\u7528\u5176\u4e2d\u7684\u51e0\u5f20\u6765\u62fc\u6210\u8f83\u5927\u7684\u7b49\u8170\u68af\u5f62,\u90a3\u4e48\u4f60\u80fd\u62fc\u51fa\u54ea\u51e0\u79cd\u4e0d\u540c\u7684\u7b49\u8170\u68af\u5f62?\u5206\u522b\u753b\u51fa\u5b83\u4eec\u7684\u793a\u610f\u56fe,\u5e76\u5199\u51fa\u5b83\u4eec\u7684\u5468\u957f.
\u89e3\uff1a\u5982\u56fe\u6240\u793a
\u516d\uff1a\u5df2\u77e5:\u5982\u56fe,\u5728\u77e9\u5f62ABCD\u4e2d,E\u3001F\u5206\u522b\u662f\u8fb9BC\u3001AB\u4e0a\u7684\u70b9,\u4e14EF=ED,EF\u22a5ED.\u6c42\u8bc1:AE\u5e73\u5206\u2220BAD.
\u8bc1\u660e\uff1a\u2235\u56db\u8fb9\u5f62ABCD\u662f\u77e9\u5f62
\u2234\u2220B=\u2220C=\u2220BAD=90\u00b0 AB=CD
\u2234\u2220BEF+\u2220BFE=90\u00b0
\u2235EF\u22a5ED\u2234\u2220BEF+\u2220CED=90\u00b0
\u2234\u2220BEF=\u2220CED\u2234\u2220BEF=\u2220CDE
\u53c8\u2235EF=ED\u2234\u25b3EBF\u224c\u25b3CDE
\u2234BE=CD
\u2234BE=AB\u2234\u2220BAE=\u2220BEA=45\u00b0
\u2234\u2220EAD=45\u00b0
\u2234\u2220BAE=\u2220EAD
\u2234AE\u5e73\u5206\u2220BAD
\u4e03\uff1a\u5982\u56fe,\u77e9\u5f62\u7eb8\u7247ABCD\u4e2d,AB=8,\u5c06\u7eb8\u7247\u6298\u53e0,\u4f7f\u9876\u70b9B\u843d\u5728\u8fb9AD\u7684E\u70b9\u4e0a,BG=10.
(1)\u5f53\u6298\u75d5\u7684\u53e6\u4e00\u7aefF\u5728AB\u8fb9\u4e0a\u65f6,\u5982\u56fe(1).\u6c42\u25b3EFG\u7684\u9762\u79ef.
(2)\u5f53\u6298\u75d5\u7684\u53e6\u4e00\u7aefF\u5728AD\u8fb9\u4e0a\u65f6,\u5982\u56fe(2).\u8bc1\u660e\u56db\u8fb9\u5f62BGEF\u4e3a\u83f1\u5f62,\u5e76\u6c42\u51fa\u6298\u75d5GF\u7684\u957f.
\u56fe\uff081\uff09
\u56fe\uff082\uff09
\u89e3:(1)\u8fc7\u70b9G\u4f5cGH\u22a5AD,\u5219\u56db\u8fb9\u5f62ABGH\u4e3a\u77e9\u5f62,\u2234GH=AB=8,AH=BG=10,\u7531\u56fe\u5f62\u7684\u6298\u53e0\u53ef\u77e5\u25b3BFG\u224c\u25b3EFG,\u2234EG=BG=10,\u2220FEG=\u2220B=90\u00b0\uff1b\u2234EH=6,AE=4,\u2220AEF+\u2220HEG=90\u00b0,\u2235\u2220AEF+\u2220AFE=90\u00b0,\u2234\u2220HEG=\u2220AFE,\u53c8\u2235\u2220EHG=\u2220A=90\u00b0,\u2234\u25b3EAF\u223d\u25b3EHG,\u2234 ,\u2234EF=5,\u2234S\u25b3EFG= EF\u00b7EG= \u00d75\u00d710=25.
(2)\u7531\u56fe\u5f62\u7684\u6298\u53e0\u53ef\u77e5\u56db\u8fb9\u5f62ABGF\u224c\u56db\u8fb9\u5f62HEGF,\u2234BG=EG,AB=EH,
\u2220BGF=\u2220EGF,\u2235EF\u2225BG\uff0c\u2234\u2220BGF=\u2220EFG,\u2234\u2220EGF =\u2220EFG,\u2234EF=EG,
\u2234BG=EF,\u2234\u56db\u8fb9\u5f62BGEF\u4e3a\u5e73\u884c\u56db\u8fb9\u5f62,\u53c8\u2235EF=EG,\u2234\u5e73\u884c\u56db\u8fb9\u5f62BGEF\u4e3a\u83f1\u5f62\uff1b
\u8fde\u7ed3BE\uff0cBE\u3001FG\u4e92\u76f8\u5782\u76f4\u5e73\u5206\uff0c\u5728Rt\u25b3EFH\u4e2d,EF=BG=10,EH=AB=8,\u7531\u52fe\u80a1\u5b9a\u7406\u53ef\u5f97FH=AF=6\uff0c\u2234AE=16\uff0c\u2234BE= =8 \uff0c\u2234BO=4 \uff0c\u2234FG=2OG=2 =4 \u3002
\u516b\uff1a\uff081\uff09\u8bf7\u7528\u4e24\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5\uff0c\u7528\u5c3a\u89c4\u5728\u6240\u7ed9\u7684\u4e24\u4e2a\u77e9\u5f62\u4e2d\u5404\u4f5c\u4e00\u4e2a
\u4e0d\u4e3a\u6b63\u65b9\u5f62\u7684\u83f1\u5f62\uff0c\u4e14\u83f1\u5f62\u7684\u56db\u4e2a\u9876\u70b9\u90fd\u5728\u77e9\u5f62\u7684\u8fb9\u4e0a\uff0e\uff08\u4fdd\u7559\u4f5c\u56fe\u75d5\u8ff9\uff09
\uff082\uff09\u5199\u51fa\u4f60\u7684\u4f5c\u6cd5\uff0e
\u89e3\uff1a\uff081\uff09\u6240\u4f5c\u83f1\u5f62\u5982\u56fe\u2460\u3001\u2461\u6240\u793a\uff0e
\u8bf4\u660e\uff1a\u4f5c\u6cd5\u76f8\u540c\u7684\u56fe\u5f62\u89c6\u4e3a\u540c\u4e00\u79cd\uff0e\u4f8b\u5982\u7c7b\u4f3c\u56fe\u2462\u3001\u56fe\u2463\u7684\u56fe\u5f62\u89c6\u4e3a\u4e0e\u56fe\u2461\u662f\u540c\u4e00\u79cd\uff0e
\uff082\uff09\u56fe\u2460\u7684\u4f5c\u6cd5\uff1a
\u4f5c\u77e9\u5f62A1B1C1D1\u56db\u6761\u8fb9\u7684\u4e2d\u70b9E1\u3001F1\u3001G1\u3001H1\uff1b
\u8fde\u63a5H1E1\u3001E1F1\u3001G1F1\u3001G1H1\uff0e
\u56db\u8fb9\u5f62E1F1G1H1\u5373\u4e3a\u83f1\u5f62\uff0e
\u56fe\u2461\u7684\u4f5c\u6cd5\uff1a
\u5728B2C2\u4e0a\u53d6\u4e00\u70b9E2\uff0c\u4f7fE2C2\uff1eA2E2\u4e14E2\u4e0d\u4e0eB2\u91cd\u5408\uff1b
\u4ee5A2\u4e3a\u5706\u5fc3\uff0cA2E2\u4e3a\u534a\u5f84\u753b\u5f27\uff0c\u4ea4A2D2\u4e8eH2\uff1b
\u4ee5E2\u4e3a\u5706\u5fc3\uff0cA2E2\u4e3a\u534a\u5f84\u753b\u5f27\uff0c\u4ea4B2C2\u4e8eF2\uff1b
\u8fde\u63a5H2F2\uff0c\u5219\u56db\u8fb9\u5f62A2E2F2H2\u4e3a\u83f1\u5f62\uff0e
A
B
C
P
D
E
\u4e5d\uff1a\u5982\u56fe\uff0cP\u662f\u8fb9\u957f\u4e3a1\u7684\u6b63\u65b9\u5f62ABCD\u5bf9\u89d2\u7ebfAC\u4e0a\u4e00\u52a8\u70b9\uff08P\u4e0eA\u3001C\u4e0d\u91cd\u5408\uff09\uff0c\u70b9E\u5728\u5c04\u7ebfBC\u4e0a\uff0c\u4e14PE=PB.
\uff081\uff09\u6c42\u8bc1\uff1a\u2460 PE=PD \uff1b \u2461 PE\u22a5PD\uff1b
\uff082\uff09\u8bbeAP=x, \u25b3PBE\u7684\u9762\u79ef\u4e3ay.
\u2460 \u6c42\u51fay\u5173\u4e8ex\u7684\u51fd\u6570\u5173\u7cfb\u5f0f\uff0c\u5e76\u5199\u51fax\u7684\u53d6\u503c\u8303\u56f4\uff1b
\u2461 \u5f53x\u53d6\u4f55\u503c\u65f6\uff0cy\u53d6\u5f97\u6700\u5927\u503c\uff0c\u5e76\u6c42\u51fa\u8fd9\u4e2a\u6700\u5927\u503c.
\u89e3\uff1a\uff081\uff09\u8bc1\u6cd5\u4e00\uff1a
\u2460 \u2235 \u56db\u8fb9\u5f62ABCD\u662f\u6b63\u65b9\u5f62\uff0cAC\u4e3a\u5bf9\u89d2\u7ebf\uff0c
\u2234 BC=DC, \u2220BCP=\u2220DCP=45\u00b0.
\u2235 PC=PC\uff0c
\u2234 \u25b3PBC\u224c\u25b3PDC \uff08SAS\uff09.
\u2234 PB= PD\uff0c \u2220PBC=\u2220PDC.
\u53c8\u2235 PB= PE \uff0c
\u2234 PE=PD.
A
B
C
D
P
E
1
2
H
\u2461 \uff08i\uff09\u5f53\u70b9E\u5728\u7ebf\u6bb5BC\u4e0a(E\u4e0eB\u3001C\u4e0d\u91cd\u5408)\u65f6\uff0c
\u2235 PB=PE\uff0c
\u2234 \u2220PBE=\u2220PEB\uff0c
\u2234 \u2220PEB=\u2220PDC\uff0c
\u2234 \u2220PEB+\u2220PEC=\u2220PDC+\u2220PEC=180\u00b0\uff0c
\u2234 \u2220DPE=360\u00b0-(\u2220BCD+\u2220PDC+\u2220PEC)=90\u00b0\uff0c
\u2234 PE\u22a5PD. \uff09
\uff08ii\uff09\u5f53\u70b9E\u4e0e\u70b9C\u91cd\u5408\u65f6\uff0c\u70b9P\u6070\u597d\u5728AC\u4e2d\u70b9\u5904\uff0c\u6b64\u65f6\uff0cPE\u22a5PD.
\uff08iii\uff09\u5f53\u70b9E\u5728BC\u7684\u5ef6\u957f\u7ebf\u4e0a\u65f6\uff0c\u5982\u56fe.
\u2235 \u2220PEC=\u2220PDC\uff0c\u22201=\u22202\uff0c
\u2234 \u2220DPE=\u2220DCE=90\u00b0\uff0c
\u2234 PE\u22a5PD.
\u7efc\u5408\uff08i\uff09\uff08ii\uff09\uff08iii\uff09, PE\u22a5PD.
A
B
C
P
D
E
F
\uff082\uff09\u2460 \u8fc7\u70b9P\u4f5cPF\u22a5BC\uff0c\u5782\u8db3\u4e3aF\uff0c\u5219BF=FE.
\u2235 AP=x\uff0cAC= \uff0c
\u2234 PC= - x\uff0cPF=FC= .
BF=FE=1-FC=1-( )= .
\u2234 S\u25b3PBE=BF\u00b7PF= ( ) .
\u5373 (0\uff1cx\uff1c ).
\u2461 .
\u2235 \uff1c0\uff0c
\u2234 \u5f53 \u65f6\uff0cy\u6700\u5927\u503c .
\uff081\uff09\u8bc1\u6cd5\u4e8c\uff1a A
B
C
P
D
E
F
G
1
2
3
\u2460 \u8fc7\u70b9P\u4f5cGF\u2225AB\uff0c\u5206\u522b\u4ea4AD\u3001BC\u4e8eG\u3001F. \u5982\u56fe\u6240\u793a.
\u2235 \u56db\u8fb9\u5f62ABCD\u662f\u6b63\u65b9\u5f62\uff0c
\u2234 \u56db\u8fb9\u5f62ABFG\u548c\u56db\u8fb9\u5f62GFCD\u90fd\u662f\u77e9\u5f62\uff0c
\u25b3AGP\u548c\u25b3PFC\u90fd\u662f\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62.
\u2234 GD=FC=FP\uff0cGP=AG=BF\uff0c\u2220PGD=\u2220PFE=90\u00b0.
\u53c8\u2235 PB=PE\uff0c
\u2234 BF=FE\uff0c
\u2234 GP=FE\uff0c
\u2234 \u25b3EFP\u224c\u25b3PGD \uff08SAS\uff09.
\u2234 PE=PD.
\u2461 \u2234 \u22201=\u22202.
\u2234 \u22201+\u22203=\u22202+\u22203=90\u00b0.
\u2234 \u2220DPE=90\u00b0.
\u2234 PE\u22a5PD.
\uff082\uff09\u2460\u2235 AP=x\uff0c
\u2234 BF=PG= \uff0cPF=1- .
\u2234 S\u25b3PBE=BF\u00b7PF= ( ) .
\u5373 (0\uff1cx\uff1c ).
\u2461 .
\u2235 \uff1c0\uff0c
\u2234 \u5f53 \u65f6\uff0cy\u6700\u5927\u503c .
\u5341\uff1a\u5982\u56fe1\uff0c\u56db\u8fb9\u5f62ABCD\u662f\u6b63\u65b9\u5f62\uff0cG\u662fCD\u8fb9\u4e0a\u7684\u4e00\u4e2a\u52a8\u70b9(\u70b9G\u4e0eC\u3001D\u4e0d\u91cd\u5408)\uff0c\u4ee5CG\u4e3a\u4e00\u8fb9\u5728\u6b63\u65b9\u5f62ABCD\u5916\u4f5c\u6b63\u65b9\u5f62CEFG\uff0c\u8fde\u7ed3BG\uff0cDE\uff0e\u6211\u4eec\u63a2\u7a76\u4e0b\u5217\u56fe\u4e2d\u7ebf\u6bb5BG\u3001\u7ebf\u6bb5DE\u7684\u957f\u5ea6\u5173\u7cfb\u53ca\u6240\u5728\u76f4\u7ebf\u7684\u4f4d\u7f6e\u5173\u7cfb\uff1a
\uff081\uff09\u2460\u731c\u60f3\u5982\u56fe1\u4e2d\u7ebf\u6bb5BG\u3001\u7ebf\u6bb5DE\u7684\u957f\u5ea6\u5173\u7cfb\u53ca\u6240\u5728\u76f4\u7ebf\u7684\u4f4d\u7f6e\u5173\u7cfb\uff1b
\u2461\u5c06\u56fe1\u4e2d\u7684\u6b63\u65b9\u5f62CEFG\u7ed5\u7740\u70b9C\u6309\u987a\u65f6\u9488(\u6216\u9006\u65f6\u9488)\u65b9\u5411\u65cb\u8f6c\u4efb\u610f\u89d2\u5ea6 \uff0c\u5f97\u5230\u5982\u56fe2\u3001\u5982\u56fe3\u60c5\u5f62\uff0e\u8bf7\u4f60\u901a\u8fc7\u89c2\u5bdf\u3001\u6d4b\u91cf\u7b49\u65b9\u6cd5\u5224\u65ad\u2460\u4e2d\u5f97\u5230\u7684\u7ed3\u8bba\u662f\u5426\u4ecd\u7136\u6210\u7acb,\u5e76\u9009\u53d6\u56fe2\u8bc1\u660e\u4f60\u7684\u5224\u65ad\uff0e
\uff082\uff09\u5c06\u539f\u9898\u4e2d\u6b63\u65b9\u5f62\u6539\u4e3a\u77e9\u5f62\uff08\u5982\u56fe4\u20146\uff09\uff0c\u4e14AB=a\uff0cBC=b\uff0cCE=ka\uff0c CG=kb (a b\uff0ck 0)\uff0c\u7b2c(1)\u9898\u2460\u4e2d\u5f97\u5230\u7684\u7ed3\u8bba\u54ea\u4e9b\u6210\u7acb\uff0c\u54ea\u4e9b\u4e0d\u6210\u7acb\uff1f\u82e5\u6210\u7acb\uff0c\u4ee5\u56fe5\u4e3a\u4f8b\u7b80\u8981\u8bf4\u660e\u7406\u7531\uff0e
\uff083\uff09\u5728\u7b2c(2)\u9898\u56fe5\u4e2d\uff0c\u8fde\u7ed3 \u3001 \uff0c\u4e14a=3\uff0cb=2\uff0ck= \uff0c\u6c42 \u7684\u503c\uff0e
\u89e3: (1)\u2460
\u2461 \u4ecd\u7136\u6210\u7acb
\u5728\u56fe\uff082\uff09\u4e2d\u8bc1\u660e\u5982\u4e0b
\u2235\u56db\u8fb9\u5f62 \u3001\u56db\u8fb9\u5f62 \u90fd\u662f\u6b63\u65b9\u5f62
\u2234 \uff0c \uff0c
\u2234
\u2234 \uff08SAS\uff09
\u2234
\u53c8\u2235
\u2234 \u2234
\u2234
\uff082\uff09 \u6210\u7acb\uff0c \u4e0d\u6210\u7acb
\u7b80\u8981\u8bf4\u660e\u5982\u4e0b
\u2235\u56db\u8fb9\u5f62 \u3001\u56db\u8fb9\u5f62 \u90fd\u662f\u77e9\u5f62\uff0c
\u4e14 \uff0c \uff0c \uff0c ( \uff0c )
\u2234 \uff0c
\u2234
\u2234
\u2234
\u53c8\u2235
\u2234 \u2234
\u2234
\uff083\uff09\u2235 \u2234
\u53c8\u2235 \uff0c \uff0c
\u2234 \u2234
\u6570\u636e\u7684\u5206\u6790\uff1a
\u4e00\uff1a4\uff0e\u4e3a\u4e86\u5e2e\u52a9\u8d2b\u56f0\u5931\u5b66\u513f\u7ae5\uff0c\u67d0\u56e2\u5e02\u59d4\u53d1\u8d77\u201c\u7231\u5fc3\u50a8\u84c4\u201d\u6d3b\u52a8\uff0c\u9f13\u52b1\u5b66\u751f\u5c06\u81ea\u5df1\u7684\u538b\u5c81\u94b1\u548c\u96f6\u82b1\u94b1\u5b58\u5165\u94f6\u884c\uff0c\u5b9a\u671f\u4e00\u5e74\uff0c\u5230\u671f\u540e\u53ef\u53d6\u56de\u672c\u91d1\uff0c\u800c\u628a\u5229\u606f\u6350\u7ed9\u8d2b\u56f0\u5931\u5b66\u513f\u7ae5.\u67d0\u4e2d\u5b66\u5171\u6709\u5b66\u751f1200\u4eba\uff0c\u56fe1\u662f\u8be5\u6821\u5404\u5e74\u7ea7\u5b66\u751f\u4eba\u6570\u6bd4\u4f8b\u5206\u5e03\u7684\u6247\u5f62\u7edf\u8ba1\u56fe\uff0c\u56fe2\u662f\u8be5\u6821\u5b66\u751f\u4eba\u5747\u5b58\u6b3e\u60c5\u51b5\u7684\u6761\u5f62\u7edf\u8ba1\u56fe.
\uff081\uff09\u4e5d\u5e74\u7ea7\u5b66\u751f\u4eba\u5747\u5b58\u6b3e\u5143\uff1b
\uff082\uff09\u8be5\u6821\u5b66\u751f\u4eba\u5747\u5b58\u6b3e\u591a\u5c11\u5143\uff1f
\uff083\uff09\u5df2\u77e5\u94f6\u884c\u4e00\u5e74\u671f\u5b9a\u671f\u5b58\u6b3e\u7684\u5e74\u5229\u7387\u662f2.25%
\uff08\u201c\u7231\u5fc3\u50a8\u84c4\u201d\u514d\u6536\u5229\u606f\u7a0e\uff09\uff0c\u4e14\u6bcf351\u5143\u80fd\u63d0\u4f9b \u7ed9\u4e00\u4f4d\u5931\u5b66\u513f\u7ae5\u4e00\u5b66\u5e74\u7684\u57fa\u672c\u8d39\u7528\uff0c\u90a3\u4e48\u8be5\u6821\u4e00\u5b66\u5e74\u80fd\u5e2e\u52a9\u591a\u5c11\u4e3a\u8d2b\u56f0\u5931\u5b66\u513f\u7ae5\u3002
\u89e3\uff1a\uff081\uff09240
\uff082\uff09 \u89e3\u6cd5\u4e00\uff1a
\u4e03\u5e74\u7ea7\u5b58\u6b3e\u603b\u989d\uff1a400\u00d71200\u00d740\uff05 = 192000\uff08\u5143\uff09
\u516b\u5e74\u7ea7\u5b58\u6b3e\u603b\u989d\uff1a300\u00d71200\u00d735\uff05 = 126000 \uff08\u5143\uff09
\u4e5d\u5e74\u7ea7\u5b58\u6b3e\u603b\u989d\uff1a 240\u00d71200\u00d725\uff05 = 72000 \uff08\u5143\uff09
\uff08192000+126000+72000\uff09\u00f7 1200 = 325 \uff08\u5143\uff09
\u6240\u4ee5\u8be5\u6821\u7684\u5b66\u751f\u4eba\u5747\u5b58\u6b3e\u989d\u4e3a 325 \u5143
\u89e3\u6cd5\u4e8c\uff1a 400\u00d740\uff05 + 300\u00d735\uff05 + 240\u00d725\uff05 = 325 \u5143
\u6240\u4ee5\u8be5\u6821\u7684\u5b66\u751f\u4eba\u5747\u5b58\u6b3e\u989d\u4e3a 325 \u5143
\uff083\uff09\u89e3\u6cd5\u4e00\uff1a \uff08192000+126000+72000\uff09\u00d72.25\uff05 \u00f7351= 25\uff08\u4eba\uff09
\u89e3\u6cd5\u4e8c\uff1a 325\u00d71200\u00d72.25\uff05\u00f7351 = 25\uff08\u4eba\uff09\u3002
\u4e8c\uff1a\u5982\u56fe\u662f\u8fde\u7eed\u5341\u5468\u6d4b\u8bd5\u7532\u3001\u4e59\u4e24\u540d\u8fd0\u52a8\u5458\u4f53\u80fd\u8bad\u7ec3\u60c5\u51b5\u7684\u6298\u7ebf\u7edf\u8ba1\u56fe\u3002\u6559\u7ec3\u7ec4\u89c4\u5b9a\uff1a\u4f53\u80fd\u6d4b\u8bd5\u6210\u7ee970\u5206\u4ee5\u4e0a\uff08\u5305\u62ec70\u5206\uff09\u4e3a\u5408\u683c\u3002
\u2474\u8bf7\u6839\u636e\u56fe11\u4e2d\u6240\u63d0\u4f9b\u7684\u4fe1\u606f\u586b\u5199\u53f3\u8868\uff1a
\u2475\u8bf7\u4ece\u4e0b\u9762\u4e24\u4e2a\u4e0d\u540c\u7684\u89d2\u5ea6\u5bf9\u8fd0\u52a8\u5458\u4f53\u80fd\u6d4b\u8bd5\u7ed3\u679c\u8fdb\u884c\u5224\u65ad\uff1a
\u2460\u4f9d\u636e\u5e73\u5747\u6570\u4e0e\u6210\u7ee9\u5408\u683c\u7684\u6b21\u6570\u6bd4\u8f83\u7532\u548c\u4e59\uff0c \u7684\u4f53\u80fd\u6d4b\u8bd5\u6210\u7ee9\u8f83\u597d\uff1b
\u5e73\u5747\u6570
\u4e2d\u4f4d\u6570
\u4f53\u80fd\u6d4b\u8bd5\u6210\u7ee9\u5408\u683c\u6b21\u6570
\u7532
65
\u4e59
60
\u2461\u4f9d\u636e\u5e73\u5747\u6570\u4e0e\u4e2d\u4f4d\u6570\u6bd4\u8f83\u7532\u548c\u4e59\uff0c \u7684\u4f53\u80fd\u6d4b\u8bd5\u6210\u7ee9\u8f83\u597d\u3002
\u2476\u4f9d\u636e\u6298\u7ebf\u7edf\u8ba1\u56fe\u548c\u6210\u7ee9\u5408\u683c\u7684\u6b21\u6570\uff0c\u5206\u6790\u54ea\u4f4d\u8fd0\u52a8\u5458\u4f53\u80fd\u8bad\u7ec3\u7684\u6548\u679c\u8f83\u597d\u3002
\u89e3\uff1a\uff081\uff09\u5982\u8868\u6240\u793a\uff1a
\u5e73\u5747\u6570
\u4e2d\u4f4d\u6570
\u4f53\u80fd\u6d4b\u8bd5\u6210\u7ee9\u5408\u683c\u6b21\u6570
\u7532
60
65
2
\u4e59
60
57.5
4
\u2475 \u2460\u4e59\uff1b\u2461\u7532
\u2476 \u4ece\u6298\u7ebf\u56fe\u4e0a\u770b\uff0c\u4e24\u540d\u8fd0\u52a8\u5458\u4f53\u80fd\u6d4b\u8bd5\u6210\u7ee9\u90fd\u5448\u4e0a\u5347\u8d8b\u52bf\uff0c\u4f46\u662f\uff0c\u4e59\u7684\u589e\u957f\u901f\u5ea6\u6bd4\u7532\u5feb\uff0c\u5e76\u4e14\u540e\u4e00\u9636\u6bb5\u4e59\u7684\u6210\u7ee9\u5408\u683c\u6b21\u6570\u6bd4\u7532\u591a\uff0c\u6240\u4ee5\u4e59\u8bad\u7ec3\u7684\u6548\u679c\u8f83\u597d\u3002
\u4e09\uff1a\u5982\u56fe\u6240\u793a\uff0cA\u3001B\u4e24\u4e2a\u65c5\u6e38\u70b9\u4ece2002\u5e74\u81f32006\u5e74\u201c\u4e94\u3001\u4e00\u201d\u7684\u65c5\u6e38\u4eba\u6570\u53d8\u5316\u60c5\u51b5\u5206\u522b\u7528\u5b9e\u7ebf\u548c\u865a\u7ebf\u8868\u793a\uff0e\u6839\u636e\u56fe\u4e2d\u6240\u793a\u89e3\u7b54\u4ee5\u4e0b\u95ee\u9898\uff1a
\uff081\uff09B\u65c5\u6e38\u70b9\u7684\u65c5\u6e38\u4eba\u6570\u76f8\u5bf9\u4e0a\u4e00\u5e74\uff0c\u589e\u957f\u6700\u5feb\u7684\u662f\u54ea\u4e00\u5e74\uff1f
\uff082\uff09\u6c42A\u3001B\u4e24\u4e2a\u65c5\u6e38\u70b9\u4ece2002\u52302006\u5e74\u65c5\u6e38\u4eba\u6570\u7684\u5e73\u5747\u6570\u548c\u65b9\u5dee\uff0c\u5e76\u4ece\u5e73\u5747\u6570\u548c\u65b9\u5dee\u7684\u89d2\u5ea6\uff0c\u7528\u4e00\u53e5\u8bdd\u5bf9\u8fd9\u4e24\u4e2a\u65c5\u6e38\u70b9\u7684\u60c5\u51b5\u8fdb\u884c\u8bc4\u4ef7\uff1b
2002 2003 2004 2005 2006 \u5e74
6
5
4
3
2
1
\u4e07\u4eba
A
B
\uff083\uff09A\u65c5\u6e38\u70b9\u73b0\u5728\u7684\u95e8\u7968\u4ef7\u683c\u4e3a\u6bcf\u4eba80\u5143\uff0c\u4e3a\u4fdd\u62a4\u65c5\u6e38\u70b9\u73af\u5883\u548c\u6e38\u5ba2\u7684\u5b89\u5168\uff0cA\u65c5\u6e38\u70b9\u7684\u6700\u4f73\u63a5\u5f85\u4eba\u6570\u4e3a4\u4e07\u4eba\uff0c\u4e3a\u63a7\u5236\u6e38\u5ba2\u6570\u91cf\uff0cA\u65c5\u6e38\u70b9\u51b3\u5b9a\u63d0\u9ad8\u95e8\u7968\u4ef7\u683c\uff0e\u5df2\u77e5\u95e8\u7968\u4ef7\u683cx\uff08\u5143\uff09\u4e0e\u6e38\u5ba2\u4eba\u6570y\uff08\u4e07\u4eba\uff09\u6ee1\u8db3\u51fd\u6570\u5173\u7cfb \uff0e\u82e5\u8981\u4f7fA\u65c5\u6e38\u70b9\u7684\u6e38\u5ba2\u4eba\u6570\u4e0d\u8d85\u8fc74\u4e07\u4eba\uff0c\u5219\u95e8\u7968\u4ef7\u683c\u81f3\u5c11\u5e94\u63d0\u9ad8\u591a\u5c11\uff1f
\u89e3\uff1a(1)B\u65c5\u6e38\u70b9\u7684\u65c5\u6e38\u4eba\u6570\u76f8\u5bf9\u4e0a\u4e00\u5e74\u589e\u957f\u6700\u5feb\u7684\u662f2005\u5e74\uff0e
(2) \uff1d \uff1d3\uff08\u4e07\u5143\uff09
\uff1d \uff1d3\uff08\u4e07\u5143\uff09 \uff1d [(-2) \uff0b(-1) \uff0b0 \uff0b1 \uff0b2 ]\uff1d2
\uff1d [0 \uff0b0 \uff0b(-1) \uff0b1 \uff0b0 ]\uff1d
\u4ece2002\u81f32006\u5e74\uff0cA\u3001B\u4e24\u4e2a\u65c5\u6e38\u70b9\u5e73\u5747\u6bcf\u5e74\u7684\u65c5\u6e38\u4eba\u6570\u5747\u4e3a3\u4e07\u4eba\uff0c\u4f46A\u65c5\u6e38\u70b9\u8f83B\u65c5\u6e38\u70b9\u7684\u65c5\u6e38\u4eba\u6570\u6ce2\u52a8\u5927\uff0e
(3)\u7531\u9898\u610f\uff0c\u5f97\u30005\uff0d \u22644 \u89e3\u5f97x\u2265100 100-80\uff1d20
\u7b54\uff1aA\u65c5\u6e38\u70b9\u7684\u95e8\u7968\u81f3\u5c11\u8981\u63d0\u9ad820\u5143\u3002
算式和思考过程都要！越详细越好！！
1.已知关于x,y的二元一次方程满足:x的系数是大于2的自然数,y的系数是小于-3的整数,且x=2,y=3是它的一个解,写出这样的一个二元一次方程(
)
2.某人买13个鸡蛋,5个鸭蛋,9个鹅蛋共用去12.8元,若买4个鸡蛋,2个鸭蛋,3个鹅蛋共用去4.7元,则买鸡蛋,鸭蛋,鹅蛋各一个共需(
)元.
3.A,B两地相距360千米,甲车从A地开往B地,每小时行驶72千米;甲车出发25分钟后,乙车从B地开往A地,每小时行驶48千米.两车相遇后各按原速度、原方向继续行驶,则甲车从出发到相遇后两车相距100千米时共行驶多少小时?
(列出二元一次方程,并解答)
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绛旓細浠ョ瓑鑵扮洿瑙掍笁瑙掑舰ABC鐨勬枩杈笰B涓庤竟闈㈠唴浣滅瓑杈光柍ABD锛岃繛缁揇C,浠C褰撹竟浣滅瓑杈光柍DCE,B銆丒鍦–銆丏鐨勫悓渚э紝鑻B=鈭2锛屾眰BE鐨勯暱銆備互绛夎叞鐩磋涓夎褰BC鐨勬枩杈笰B涓鸿竟鍚戝唴浣滅瓑杈光柍ABD锛屾垜璁や负C銆丏鍦ˋB鍚屼晶銆傚欢闀緿C浜B浜嶦锛屽彲鐭E鍨傜洿骞冲垎AB锛孌E骞冲垎瑙扐DB锛岃CDE=瑙扖DB+瑙払DE=60搴︼紝瑙扖DB=瑙払DE=...
绛旓細鍒濅簩鐨鏁板棰樼洰1.AD骞宠BC锛岃B锛濊C锛孉E锛滸F锛滸C銆 姹傝瘉锛氬綋瑙扚GC锛2瑙扙FB鏃讹紝鍥涜竟褰EFG鏄煩褰 鍥撅細
