六年级数学题,在长方形中画圆,学霸们能帮我解一下吗

\u5173\u4e8e\u5706\u7684\u5965\u6570\u9898\u516d\u5e74\u7ea7\u7684

\u6709\u4e24\u4e2a\u5706\u5916\u5207\uff0c\u5706\u5fc3\u8ddd\u4e3a7cm\uff0c\u5185\u5207\u65f6\u5706\u5fc3\u8ddd\u4e3a1cm\uff0c\u5219\u4e24\u5706\u7684\u534a\u5f84\u5206\u522b\u662f\u591a\u5c11\uff1f


\u628a\u4e00\u4e2a\u5706\u7b49\u5206\u540e\u62fc\u6210\u4e00\u4e2a\u8fd1\u4f3c\u4e8e\u957f\u65b9\u5f62\uff0c\u5df2\u77e5\u62fc\u6210\u540e\u7684\u8fd9\u4e2a\u957f\u65b9\u5f62\u7684\u5468\u957f\u6bd4\u5706\u5468\u957f\u957f6\u5398\u7c73\u3002\u6c42\u8fd9\u4e2a\u5706\u7684\u5468\u957f\u548c\u9762\u79ef

\u5df2\u77e5A(0,1)B(2,1)C(3,4)D(-1,2) \u56db\u70b9 \u95ee\u4ed6\u4eec\u662f\u5426\u5728\u4e00\u4e2a\u5706\u4e0a

\u5df2\u77e5\uff1a\u4e09\u89d2\u5f62ABC\u5185\u63a5\u4e0e\u5706o\uff0c\u70b9D\u5728OC\u7684\u5ef6\u957f\u7ebf\u4e0a\uff0csinb=1/2\uff0c\u2220D=30\u00b0
1.\u6c42\u8bc1\uff1aAD\u662f\u5706O\u7684\u5207\u7ebf
2.\u82e5AC=6\uff0c\u6c42AD\u957f

\u5df2\u77e5\u52a8\u5706\u8fc7\u70b9F\uff08\uff0d5\uff0c0\uff09\u4e14\u4e0e\u5706x*x+y*y-10x-11=0\u76f8\u5207\uff0c\u6c42\u52a8\u5706\u5706\u5fc3\u7684\u8f68\u8ff9\u65b9\u7a0b\uff0e

\u25ce \u5de6\u9762\u662f\u4e00\u4e2a\u73af\u5f62\u3002\u5b83\u7684\u5185\u5706\u534a\u5f84\u662f10\u5398\u7c73\uff0c\u5916\u5706\u534a\u5f84\u662f15\u5398\u7c73\u3002\u5b83\u7684\u9762\u79ef\u662f\u591a\u5c11\uff1f

\u60f3\uff1a\u8fd9\u4e2a\u73af\u5f62\u7684\u9762\u79ef\u5b9e\u9645\u5c31\u662f\u4e24\u4e2a\u5706\u9762\u79ef\u7684\uff08 \uff09\u3002

\u2474\u5916\u5706\u9762\u79ef\uff1a

\u2475\u5185\u5706\u9762\u79ef\uff1a

\u2476\u73af\u5f62\u7684\u9762\u79ef\uff1a


\u6ce8\uff08x\uff0cy\u540e\u7684\u6570\u4f4d\u5e73\u65b9\uff09


\u5df2\u77e5\u5706C\uff1ax2+y2+2x+ay-3=0\uff08a\u4e3a\u5b9e\u6570\uff09\u4e0a\u4efb\u610f\u4e00\u70b9\u5173\u4e8e\u76f4\u7ebfL\uff1ax-y+2=0\u7684\u5bf9\u79f0\u70b9\u90fd\u5728\u5706C\u4e0a\u5219a\u7b49\u4e8e\u591a\u5c11

\u5df2\u77e5\u25b3ABC\u5185\u63a5\u4e8e\u25cbO\uff0c\u70b9D\u5728OC\u7684\u5ef6\u957f\u7ebf\u4e0a\uff0csinB=½\uff0c\u2220D=30\u00b0\uff081\uff09\u6c42\u8bc1\uff1aAD\u662f\u25cbO\u7684\u5207\u7ebf\uff082\uff09\u82e5AC=6,\u6c42AD\u7684\u957f

\u5df2\u77e5\u6b63\u516d\u8fb9\u5f62\u7684\u8fb9\u5fc3\u8ddd\u4e3aa\uff0c\u90a3\u4e48\u5b83\u7684\u8fb9\u957f\u4e3a \u3002
\u82e5\u5706\u67f1\u7684\u4fa7\u9762\u5c55\u5f00\u56fe\u662f\u4e00\u4e2a\u8fb9\u957f\u4e3a4cm\u7684\u6b63\u65b9\u5f62\uff0c\u5219\u5706\u67f1\u5e95\u9762\u5706\u7684\u534a\u5f84= \u3002
\u82e5\u4e00\u4e2a\u6b63\u65b9\u5f62\u7684\u5185\u5207\u5706\u7684\u9762\u79ef\u662f\u03c0cm2\uff0c\u5219\u5b83\u7684\u5916\u63a5\u5706\u9762\u79ef\u662f \u3002



1.\u5df2\u77e5A\uff08\uff0d2\uff0c0\uff09\uff0cB\uff080\uff0c2\uff09\uff0cC\u662f\u5706X^2+Y^2-2X=0\u4e0a\u4efb\u610f\u4e00\u70b9\uff0c\u5219\u4e09\u89d2\u5f62ABC\u9762\u79ef\u7684\u6700\u5927\u503c\u662f\uff1f
2.\u82e5\u76f4\u7ebf2ax\uff0dby+2=0(a>0,b>0)\u59cb\u7ec8\u5e73\u5206\u5706x^2+y^+2x-4y+1=0\u7684\u5468\u957f\uff0c\u52191/a+1/b\u7684\u6700\u5c0f\u503c\u662f


cd\u662f\u5706o\u7684\u76f4\u5f84,\u4ee5d\u4e3a\u5706\u5fc3,od\u7684\u957f\u4e3a\u534a\u5f84\u4f5c\u5f27,\u4ea4\u5706o\u4e8e\u4e24\u70b9a b \u6c42\u8bc1\u5f27ac=cb=ab

\u4e00\u4e2a\u5706\u67f1\u5f62\u6c34\u6876\uff0c\u5e95\u9762\u76f4\u5f84\u662f28\u5398\u7c73\uff0c\u9ad8\u662f60\u5398\u7c73\u3002\u5df2\u77e5\u6bcf\u5347\u6c34\u91cd1\u5343\u514b\uff0c\u8fd9\u4e2a\u6c34\u6876\u5927\u7ea6\u80fd\u76db\u6c34\u591a\u5c11\u5343\u514b


1\u3002\u4ece\u5706\u5916\u4e00\u70b9\u5f15\u4e24\u6761\u5207\u7ebf\u4e92\u76f8\u5782\u76f4\uff0c\u8fd9\u70b9\u4e0e\u5706\u5fc3\u7684\u8ddd\u79bb\u4e3a4\uff0c\u5219\u5706\u7684\u534a\u5f84\u4e3a\uff1f
2\u3002\u5706O\u5207\u4e09\u89d2\u5f62ABC\u7684BC\u8fb9\u4e8eD\uff0c\u5207AB\u3001AC\u7684\u5ef6\u957f\u7ebf\u4e8eE\u3001F\uff0c\u4e09\u89d2\u5f62ABC\u7684\u5468\u957f\u4e3a18\uff0c\u5219AE=\uff1f
3\u3002\u5706\u67f1\u7684\u5730\u9762\u534a\u5f84\u4e3a3\uff0c\u6bcd\u7ebf\u957f\u4e3a3\uff0c\u90a3\u4e48\u8fd9\u4e2a\u5706\u67f1\u7684\u4fa7\u9762\u5c55\u5f00\u56fe\u7684\u9762\u79ef\u662f\uff1f
4\u3002\u4e00\u4e2a\u5706\u9525\u7684\u9ad8\u4e3a3\u500d\u6839\u53f73\uff0c\u4fa7\u9762\u5c55\u5f00\u56fe\u662f\u534a\u5706\uff0c\u6c42\uff1a\u5706\u9525\u7684\u6bcd\u7ebf\u4e0e\u5730\u9762\u534a\u5f84\u4e4b\u6bd4\uff1b\u9525\u89d2\u7684\u5927\u5c0f\uff1b\u5706\u9525\u7684\u8868\u9762\u79ef\uff08\u6b64\u9898\u8981\u8fc7\u7a0b\uff09



Rt\u25b3ABC\u4e2d,\u2220CAB=30\u00b0,BC=2,O,H\u5206\u522b\u4e3a\u8fb9AB,AC\u7684\u91cd\u70b9,\u5c06\u25b3ABC\u9976\u70b9B\u987a\u65f6\u9488\u65cb\u8f6c120\u5ea6\u5230\u4e09\u89d2\u5f62A1BC1\u5904\u7684\u4f4d\u7f6e,\u5219\u6574\u4e2a\u65cb\u8f6c\u8fc7\u7a0b\u4e2d\u7ebf\u6bb5OH\u626b\u8fc7\u90e8\u5206\u7684\u9762\u79ef,(\u9634\u5f71\u9762\u79ef)

\u5df2\u77e5\u70b9p\u5728\u7ebf\u6bb5AB\u4e0a\uff0c\u70b9o\u5728\u7ebf\u6bb5AB\u5ef6\u957f\u7ebf\u4e0a\u3002\u4ee5\u70b9o\u4e3a\u5706\u5fc3\uff0cop\u4e3a\u534a\u5f84\u505a\u5706\uff0c\u70b9c\u53f2\u5706o\u4e0a\u4e00\u70b9\u3002
\u5982\u679cAP=m\uff0cm\u662f\u5e38\u6570\uff0c\uff1e1\uff0cBP=1\uff0cop\u662fOA OB\u7684\u6bd4\u4f8b\u4e2d\u9879\uff0c\u5f53\u70b9c\u5728\u5706o\u4e0a\u8fd0\u52a8\u65f6\uff0c\u6c42AC\uff1aBC \u7528m\u7684\u5f0f\u5b50\u8868\u793a

\u5982\u56fe\uff1a\u5df2\u77e5\u77e9\u5f62ABCD\u7684\u8fb9AB\u7ecf\u8fc7\u5706\u5fc3O\uff0c\u70b9E\u3001F\u5206\u522b\u662f\u8fb9AB\u3001CD\u4e0e\u5706O\u7684\u4ea4\u70b9\uff0cAE=3\u5398\u7c73\uff0cAD=4\u5398\u7c73\uff0cDF=5\u5398\u7c73\uff0c\u6c42\u5706O\u7684\u76f4\u5f84\u957f\u3002

\u5df2\u77e5\u70b9A\u662f\u5706O\u4e0a\u7684\u4e00\u4e2a\u516d\u7b49\u5206\u70b9\uff0c\u70b9B\u662f\u5f27AN\u7684\u4e2d\u70b9\uff0c\u70b9P\u662f\u534a\u5f84ON\u4e0a\u7684\u4e00\u52a8\u70b9\uff0c\u82e5\u5706O\u7684\u534a\u5f84\u957f\u4e3a1\uff0c\u6c42AP+BP\u7684\u6700\u5c0f\u503c


\u5982\u56fe,\u4e09\u89d2\u5f62ABC\uff0c\u89d2ACB=90\u00b0\uff0c\u89d2B=60\u00b0\uff0cCD\u22a5AB\uff0c\u5782\u8db3\u4e3aD,BD=\u6839\u53f73,\u4ee5C\u4e3a\u5706\u5fc3\uff0c2\u53c8\u6839\u53f73\u4e3a\u534a\u5f84\u5de6\u5706C\uff0c\u8bd5\u5206\u522b\u5224\u65adA.D.B\u4e09\u70b9\u4e0e\u5706C\u7684\u4f4d\u7f6e\u5173\u7cfb


1.\u76f4\u89d2\u4e09\u89d2\u5f62\u4e24\u8fb9\u957f\u5206\u522b\u4e3a5cm\u548c12cm\uff0c\u6c42\u5b83\u7684\u5916\u63a5\u5706\u5468\u957f\u548c\u5185\u5207\u5706\u5f97\u9762\u79ef

2\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62\u5185\u5207\u5706\u5f97\u534a\u5f84\u4e0e\u5916\u5207\u5706\u7684\u534a\u5f84\u4e4b\u6bd4\u662f\uff1f

\u5df2\u77e5\u2299\u25cb1\u4e0e\u2299\u25cb2\u76f8\u4ea4\u4e8eA\u3001B\u4e24\u70b9\uff0c\u4e14\u5706\u5fc3\u25cb1\u5728\u2299\u25cb2\u4e0a\uff0c\u8fc7\u70b9A\u4f5c\u2299\u25cb1\u7684\u5207\u7ebfAC\u4ea4B\u25cb1\u7684\u5ef6\u957f\u7ebf\u4e8e\u70b9P\uff0c\u4ea4\u2299\u25cb2\u4e8e\u70b9C\uff0cBP\u4ea4\u2299\u25cb1\u4e8e\u70b9D\uff0cPD=1\uff0cPA=\u6839\u53f75.\uff081)\u6c42\u2299\u25cb1\u7684\u534a\u5f84\uff1b\uff082)\u4f60\u53d1\u73b0\u25b3PBC\u662f\u4ec0\u4e48\u5f62\u72b6\u7684\u4e09\u89d2\u5f62\uff1f\u8bf7\u5199\u51fa\u53d1\u73b0\u7684\u7ed3\u8bba\u5e76\u8fdb\u884c\u8bc1\u660e\u3002


\u5df2\u77e5AB\u662f\u2299O\u7684\u76f4\u5f84\uff0cAE\u5e73\u5206<BAF\uff0c\u4ea4\u2299O\u4e8e\u70b9E\uff0c\u8fc7\u70b9E\u4f5c\u76f4\u7ebfED\u22a5AF\uff0c\u4ea4AF\u7684\u5ef6\u957f\u7ebf\u4e8e\u70b9D\uff0c\u4ea4AB\u7684\u5ef6\u957f\u7ebf\u4e8e\u70b9C\u3002
\uff081\uff09\u6c42\u8bc1\uff1aCD\u662f\u2299O\u7684\u5207\u7ebf\u3002
\uff082\uff09\u82e5CB=2\uff0cCE=4\uff0c\u6c42AE\u7684\u957f\u3002


\u5df2\u77e5\u5706O1\u548c\u5706O2\u7684\u534a\u5f84\u957f\u5206\u522b\u4e3aR\u548cr\uff08R\u5927\u4e8er\uff09\uff0c\u5706\u5fc3\u8ddd\u4e3ad\uff0c\u82e5\u4e24\u5706\u76f8\u4ea4\uff0c\u8bd5\u5224\u5b9a\u5173\u4e8ex\u7684\u65b9\u7a0b\uff1a\uff08x\u5e73\u65b9\uff09-2\uff08d-R\uff09x+\uff08r\u5e73\u65b9\uff09=0\u7684\u6839\u7684\u60c5\u51b5\u3002


\u5728RT\u25b3ABC,\u89d2C=90\u00b0 \u89d2B=30\u00b0 ,O\u662fAB\u4e0a\u7684\u4e00\u70b9,OA=m,\u5706O\u7684\u534a\u5f84\u4e3ar,\u5f53r\u4e0em\u6ee1\u8db3\u4ec0\u4e48\u7684\u5173\u7cfb\u65f6:

AC\u4e0e\u5706O\u76f8\u4ea4?
AC\u4e0e\u5706O\u76f8\u5207?
AC\u4e0e\u5706O\u76f8\u79bb?

\u4ece\u201c\u6b63\u65b9\u5f62\u7684\u9762\u79ef\u662f5\u5e73\u65b9\u5398\u7c73,\u5706\u7684\u534a\u5f84\u6070\u597d\u662f\u6b63\u65b9\u5f62\u7684\u8fb9\u957f\u201d\u53ef\u5f97\u77e5\u201c5\u201d\u65e2\u53ef\u4ee5\u8868\u793a\u6b63\u65b9\u5f62\u9762\u79ef\uff0c\u53c8\u7b49\u4e8e\u5706\u7684R\u5e73\u65b9\u3002\u6240\u4ee5\uff0c\u5706\u9762\u79ef=5\u00d73.14=15.7\uff08\u5e73\u65b9\u5398\u7c73\uff09
15.7-5=10.7\uff08\u5e73\u65b9\u5398\u7c73\uff09
\u7b54\uff1a\u5706\u7684\u9762\u79ef\u6bd4\u6b63\u65b9\u5f62\u9762\u79ef\u592710.7\u5e73\u65b9\u5398\u7c73\u3002

提示:

      如果没有其它条件限制,就可以比较随意的作图。

但必须自己动手,会用圆规画圆。同时培养了适当处理

画圆的大小、位置的能力。方法很多,仅例如图:

希望对你有帮助!



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    绛旓細4銆佸渾鏄酱瀵圭О鍥惧舰锛屾湁鏃犳暟鏉″绉拌酱锛屽绉拌酱灏辨槸鐩村緞銆5銆佸渾蹇冨喅瀹氬渾鐨勪綅缃紝鍗婂緞鍐冲畾鍦嗙殑澶у皬銆6銆佹鏂瑰舰閲屾渶澶х殑鍦嗐備袱鑰呰仈绯伙細杈归暱锛濈洿寰 锛堝湪涓嬮潰姝f柟褰㈤噷鐢讳竴鐢伙級鐢绘硶锛氾紙1锛夌敾鍑烘鏂瑰舰鐨勪袱鏉″瑙掔嚎锛涳紙2锛変互瀵硅绾夸氦鐐逛负鍦嗗績锛屼互杈归暱涓虹洿寰鐢诲渾銆7銆闀挎柟褰閲屾渶澶х殑鍦嗐備袱鑰呰仈绯伙細瀹...
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    绛旓細寰堢畝鍗曠殑锛屼綘鐪嬪涓嶅鍛锛氬厛绠楀嚭杈归暱锛32梅4=8鍘樼背 鐒跺悗閫氳繃杈归暱姹傛鏂瑰舰鐨勯潰绉細8脳8=64骞虫柟鍘樼背 瑕佺敾4涓鍦嗭紝灏辨妸姝f柟褰㈠钩鍧囧垎鎴4浠斤細64梅4=16鍘樼背 鐭ラ亾灏忔鏂瑰舰鐨勯潰绉紝鍙互姹傚嚭杈归暱锛屼篃灏辨槸鍦嗙殑鐩村緞锛4脳4=16鍘樼背 鍗婂緞灏辨槸4梅2=2鍘樼背 鐩村埌鍗婂緞锛屽氨鐢細3銆14脳锛2脳2锛=12銆56骞虫柟...
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