已知a,b,c为球o的球面上三个点,o1为三角形上abc上的外接圆的点
答案: R ∵AB的中点为△ABC的外接圆心O′ ∴OO′=R 2 -( .绛旓細绛旀锛 R 鈭AB鐨涓偣涓衡柍ABC鐨勫鎺ュ渾蹇僌鈥 鈭OO鈥=R 2 -( .
绛旓細DO22脳CO脳CD=12+4?122脳23脳2=36鏁呯瓟妗堜负锛36
绛旓細鍦ㄢ柍ABC涓紝鈭礎B=2锛孊C=4锛屼笖鈭燗BC=60掳锛屸埓AC=AB2+BC2?2?AB?BC?cos鈭燗BC=4+16?8=23锛岀敱姝e鸡瀹氱悊鍙緱骞抽潰ABC鎴悆鎵寰楀渾鐨勫崐寰勶紙鍗斥柍ABC鐨勫鎺ュ渾鍗婂緞锛夛紝r=AC2sin鈭燗BC=2锛屽張鈭电悆蹇冨埌骞抽潰ABC鐨勮窛绂籨=3锛鈭鐞僌鐨鍗婂緞R=r2+d2=7锛屾晠鐞僌鐨勮〃闈㈢НS=4蟺R2=28蟺锛屾晠绛旀涓猴細28蟺锛
绛旓細鐢遍鎰A銆丅銆丆鏄悆O鐨勭悆闈笂涓夌偣锛屼笁妫遍敟O-ABC鐨勯珮涓22涓斺垹ABC=60掳锛孉B=2锛孊C=4锛屽嵆cos鈭燗BC=12=ABBC锛屽彲鐭ュ簳闈笁瑙掑舰鏄洿瑙掍笁瑙掑舰锛屾枩杈逛腑鐐逛笌鐞冨績鐨勮繛绾匡紝灏辨槸妫遍敟鐨勯珮锛屾墍浠ョ悆鐨勫崐寰勪负锛22+(22)2=23锛屾墍浠ョ悆鐨勮〃闈㈢Н涓猴細4蟺(23)2=48蟺锛庢晠閫塀锛
绛旓細C 璇曢鍒嗘瀽锛氱敱 锛屽垯 锛岃 鐨勫鎺ュ渾鍗婂緞涓 锛屽垯 锛屽嵆 锛 锛 .
绛旓細璇曢鍒嗘瀽锛氳繃 浣 鐨勫瀭绾匡紝鍨傝冻涓 锛屼互 鎵鍦ㄧ嚎涓 杞达紝浠 鎵鍦ㄧ嚎涓 杞达紝浠 鎵鍦ㄧ嚎涓 杞达紝寤虹珛鐩磋鍧愭爣绯伙紝鎵浠 锛 锛 锛 锛 锛 锛屾墍浠 .
绛旓細骞抽潰ABC涓鐞冮潰鐨勫垏闈㈡槸涓涓渾銆侫BC涓鐐瑰潎鍦ㄨ繖涓渾鍛ㄤ笂銆傚洜涓轰笁瑙掑舰ABC鏄竴涓洿瑙掍笁瑙掑舰锛屾墍浠C鏄鍦嗙殑鐩村緞銆傜悆蹇僶鍒板钩闈BC鐨鍨傝冻鑲畾鍦˙C鐨勪腑鐐广傛墍浠锛岀悆鐨鍗婂緞涓烘牴鍙(11+5^2)=鏍瑰彿36=6 鐞冪殑浣撶Н涓4PI*6^3/3=288PI
绛旓細O鏄瓑杈光柍ABC鐨勯噸蹇 鈭OC=2/3OH 鈭寸瓑杈逛笁瑙掑舰ABC鐨勯珮OH=3鈭3/2 AC=3鈭3/2/sin60掳=3 涓夋1閿-ABC浣撶Н=1/3*PO*S鈻矨BC=1/3*3*1/2*3鈭3/2*3=9鈭3/4 濡傛灉鏈鏈変粈涔堜笉鏄庣櫧鍙互杩介棶锛屽鏋滄弧鎰忚寰楅噰绾冲鏋滄湁鍏朵粬闂璇峰彟鍙戞垨鐐瑰嚮鍚戞垜姹傚姪锛岀瓟棰樹笉鏄擄紝璇疯皡瑙o紝璋㈣阿銆傜瀛︿範杩涙锛
绛旓細瑙g瓟锛氳В锛鐞冮潰涓婁笁鐐笰銆丅銆丆锛屽钩闈BC涓庣悆闈氦浜庝竴涓渾锛屼笁鐐笰銆丅銆丆鍦ㄨ繖涓渾涓娾埖AB=18锛孊C=24锛孉C=30锛孉C2=AB2+BC2锛屸埓AC涓杩欎釜鍦嗙殑鐩村緞锛孉C涓偣M鍦嗗績鐞冨績O鍒板钩闈BC鐨璺濈鍗砄M=鐞冨崐寰勭殑涓鍗=12R鈻砄MA涓紝鈭燨MA=90掳锛孫M=12R锛孉M=12AC=30脳12=15锛孫A=R鐢卞嬀鑲″畾鐞嗭紙12R锛2+152...
绛旓細鈭鐞冮潰闈㈢НS=20蟺=4蟺R 2 锛屸埓R 2 =5鈭礎C鈯BC锛涓擜B=2锛屸埓鈻矨BC涓浠涓虹洿瑙掔殑鐩磋涓夎褰⑩埓骞抽潰ABC鎴悆寰楀埌鐨勬埅闈㈠渾鍗婂緞r= 1 2 AB=1鈭寸悆蹇僌鍒板钩闈BC鐨璺濈d= R 2 - r 2 =2鏁呯瓟妗堜负锛2