一道高中数学几何题……求解 一道高中数学几何问题，求解！！！
\u4e00\u9053\u9ad8\u4e2d\u6570\u5b66\u51e0\u4f55\u9898\uff01\u6c42\u89e3\uff01CP=CQ=2\u221a3,CR=(3\u221a3)/2,
\u6240\u4ee5\u4e09\u89d2\u5f62CPQ\u7684\u9ad8CH=\u221a((\u30162\u221a(3))\u3017^2-(\u30163/4 \u221a3)\u3017^2 )=\u221a165/4
Scpq=1/2•(3\u221a3)/2•\u221a165/4=(9\u221a55)/16
Vc-pqr=1/3•(9\u221a55)/16•h=4\u221a3\uff0ch=(64\u221a3)/(3\u221a55)
\u5728word\u91cc\u9762\u7f16\u8f91\u7684\u6839\u53f7\u5728\u8fd9\u91cc\u65e0\u6cd5\u663e\u793a\u5b8c\u6574\uff0c\u4f60\u8bd5\u7740\u770b\u5427\u3002
\u6211\u7528\u7684\u662f\u5411\u91cf\u7684\u65b9\u6cd5\uff1a
\uff083\uff09\u89e3\uff1a\u4ee5A\u4e3a\u539f\u70b9\uff0cAB\u3001AD\u3001AA1\u6240\u5728\u76f4\u7ebf\u5206\u522b\u4e3ax\u3001y\u3001z\u8f74 \u8bbeAB1\u957f\u4e3aa\uff08a>0\uff09
\u5219A\uff080\u30010\u30010\uff09 B1\uff08a\u30010\u30011\uff09 E\uff08a/2\u30011\u30010\uff09 A1\uff080\u30010\u30011\uff09B\uff08a\u30010\u30010\uff09
\u5219B1E\uff08\u5411\u91cf\uff09=\uff08-a/2\u30011\u3001-1\uff09 AB1\uff08\u5411\u91cf\uff09=\uff08a\u30010\u30011\uff09
A1B1\uff08\u5411\u91cf\uff09=\uff08a\u30010\u30010\uff09\u8bbe\u5e73\u9762AB1E\u3001\u5e73\u9762A1B1E\u7684\u6cd5\u5411\u91cf\u5206\u522b\u4e3a\uff1a
n1\uff08\u5411\u91cf\uff09=\uff08x1\u3001y1\u3001z1\uff09 n2\uff08\u5411\u91cf\uff09=\uff08x2\u3001y2\u3001z2\uff09
\u7531\u6b64\u53ef\u5f97B1E\uff08\u5411\u91cf\uff09\u00d7 n1\uff08\u5411\u91cf\uff09=AB1\uff08\u5411\u91cf\uff09\u00d7 n1\uff08\u5411\u91cf\uff09=0
B1E\uff08\u5411\u91cf\uff09\u00d7 n2\uff08\u5411\u91cf\uff09=A1B1\uff08\u5411\u91cf\uff09\u00d7 n2\uff08\u5411\u91cf\uff09=0
\u53ca-a/2x1+y1-z1=0 ax1+z1=0 \u89e3\u5f97-a/2x1=y1=z/2 \u53e6X1=2/a
\u5f97\u5230n1\uff08\u5411\u91cf\uff09=\uff082/a\u3001-2\u3001-1\uff09
-a/2x2+y2-z2=0 ax2=0 \u89e3\u5f97x2=0\u4e14y2=z2 \u53e6y2=1
\u5f97\u5230n2\uff08\u5411\u91cf\uff09=\uff080\u30011\u30011\uff09
\u8bbe\u4e8c\u9762\u89d2\u4e3a\u03b1 \u5219\u03b1=30\u00b0 \u6240\u4ee5cos\u03b1=\u4e28cos\u4e28=\u221a3/2
\u53ca3/\u221a(a²/4+5)\u00d7\u221a2=\u221a3/2 \u89e3\u5f97a=2
\u6240\u4ee5AB\uff08\u5411\u91cf\uff09=\uff082\u30010\u30010\uff09 \u6545AB\u957f\u4e3a2
\u54ea\u8fb9\u4e0d\u61c2\u53ef\u4ee5\u518d\u95ee\u6211\u3002
如图
计算量有点大，纸不够用😂是个压轴题。
如图，如有疑问或不明白请追问哦！如经常需要问此类问题，可以点个关注哦。
解法2本想套用一个公式，结果发现那个公式是错误的，公式出处：
zhidao.baidu.com/question/1931052707155817107.html?entry=uhome_homecenter_recommend
2倍根号2
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绛旓細鍋囪杩囩洿绾縓=4涓婄殑涓鐐规槸M鍧愭爣鏄:(xM,yM)=(4,y0)A鍧愭爣鏄(xA,yA)B鍧愭爣鏄(xB,yB)閭ｄ箞AM鐨勬柟绋嬩负锛堝弬鐪嬫き鍦嗗垏绾挎柟绋嬶級(xA/4)*x+yA*y/3=1 BM鐨勬柟绋嬩负 (xB/4)*x+yB*y/3=1 涓ょ洿绾块兘缁忚繃M 鎵浠,鍙互鎶奙鐨勫潗鏍囦唬杩涘幓锛屽緱鍒 (xA/4)*xM+yA*yM/3=1 (xB/4)*xM+yB*yM/3=1 鏋...
绛旓細鍗虫棤璁簁鍙栦綍鍊兼椂锛岃鐩寸嚎y=-3x+k/2閮戒笌y=-3x/2骞宠鎴栬呴噸鍚堛傚洜涓簒,y鍙堟弧瓒(x-2)²+y²=3锛屾墍浠ュ彉鐩哥粰鍑轰簡x,y鐨勫彇鍊艰寖鍥淬傚鍥撅細褰撶洿绾縴=-3x/2+k/2鍙朆鐐规椂锛屽嵆灏嗚鐩寸嚎骞崇Щ鍒癇鐐规椂k鍊兼渶澶с傚叿浣撳仛娉曞涓嬪浘锛氱浜岄鍚岀悊鍙瘉銆傚叿浣撳仛娉曞鍥撅細甯屾湜瀵逛綘鏈夋墍甯姪锛
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绛旓細瑙ｏ細1銆佸湪涓夋１鏌盇BC-A1B1C1涓紝AA1鈭B1 鍒欌垹B1BC鎴栧叾琛ヨ鍗充负鎵姹 鍦ㄢ柍ABC涓紝AB鈯ヤ笖锛滱C锛屽垯BC=2*2½鍚岀悊锛孊1C1=2*2½鍦ㄢ柍A1BC1涓紝A1B=A1C1=2锛屽張A1B鈯ラ潰ABC 鍒橞C1=2*2½鍦ㄢ柍ABA1涓紝AB鈯ヤ笖=A1B 鍒橝A1=2*2½鍒欏湪涓夋１鏌盇BC-A1B1C1涓 AA1=BB1=...
绛旓細鏇茬嚎C2锛歽锛坹-mx-m锛=0琛ㄧず涓ゆ潯鐩寸嚎y=0鍜寉-mx-m=0 杩欐牱鐞嗚В锛氭洸绾緾2涓婄殑鐐瑰寘鎷洿绾縴=0涓婄殑鐐瑰拰鐩寸嚎y-mx-m=0涓婄殑鐐逛袱閮ㄥ垎銆傜洿绾縴=0涓婄殑鐐瑰拰鐩寸嚎y-mx-m=0閮藉垎鍒槸鏇茬嚎C2涓婄殑鐐圭殑涓閮ㄥ垎銆傛洸绾緾1涓庢洸绾緾2浜ょ偣鐢盋1涓庣洿绾縴=0鐨勪氦鐐瑰拰C1涓庣洿绾縴-mx-m=0鐨勪氦鐐圭粍鎴 C1锛(X-1)2+Y2=...
绛旓細渚濋鎰忥細1/cos^2鈭燩F1F2=(PF1)^2/(c-Px)^2=1+(4cPx)/(c-Px)^2=(7/5)^2=1+24/25 4cPx*25=24(c^2-2cPx+Px^2); 6Px^2-37cPx+6c^2=(Px-6c)(6Px-c)=0 Px1=6c,Px2=c/6;6cb^2=2ca^2+a(2a^2+b^2); 2c(3b^2-a^2)=a(2a^2+b^2)...(4);寰...
绛旓細鐢扁垹ACB=90掳(鐩村緞涓婄殑鍦嗗懆瑙)寰楀埌OM鈯B 鐢盓涓篜B鐨勪腑鐐瑰緱鍒癊O鈭A鈯,EO鈯B 鎵浠ュ钩闈MO鈯B鈯CB 杩囩偣M浣淎C鐨勫瀭绾夸氦AC鐨勫欢闀跨嚎浜嶧,杩囩偣O浣淎C鐨勫瀭绾夸氦AC浜嶨 鐢扁垹ACB=90掳OM鈭C,寰楀埌O涓篈B鐨勪腑鐐 G涓篈C鐨勪腑鐐筂F=OG=AOCOS30掳=鈭3/2AO 鐢監M鈭C寰楀埌鈭燙AB=鈭燨MB,鈭燤OB=120掳,OM=...
