如图,直线MN与线段AB相交于点O,点C和点D在直线MN上,且∠ACN=∠BDN=45°(1)如图1所示,当点C与点O重 如图,AB是⊙O的直径,C是⊙0上的一点,直线MN经过点C,...
\u5728\u56fe1\u81f3\u56fe3\u4e2d\uff0c\u76f4\u7ebfMN\u4e0e\u7ebf\u6bb5AB\u76f8\u4ea4\u4e8e\u70b9O\uff0c\u22201=\u22202=45\u00b0\u3002 \uff081\uff09\u5982\u56fe1\uff0c\u82e5AO=OB\uff0c\u8bf7\u5199\u51faAO\u4e0e\u89e3\uff1a\uff081\uff09AO=BD\uff0cAO\u22a5BD\uff1b\uff082\uff09\u8bc1\u660e\uff1a\u5982\u56fe4\uff0c\u8fc7\u70b9B\u4f5cBE\u2225CA\u4ea4DO\u4e8eE\uff0c\u2234\u2220ACO=\u2220BEO\u53c8\u2235AO=OB\uff0c\u2220AOC=\u2220BOE\uff0c\u2234\u25b3AOC\u224c\u25b3BOE\uff0c\u2234AC=BE\uff0c\u53c8\u2235\u22201=45\u00b0\uff0c\u2234\u2220ACO=\u2220BEO=135\u00b0\uff0c\u2234\u2220DEB=45\u00b0\uff0c\u2235\u22202=45\u00b0\uff0c\u2234BE=BD\uff0c\u2220EBD=90\u00b0\uff0c\u2234AC=BD\uff0c\u5ef6\u957fAC\u4ea4DB\u7684\u5ef6\u957f\u7ebf\u4e8eF\uff0c\u5982\u56fe4\uff0c\u2235BE\u2225AC\uff0c\u2234\u2220AFD=90\u00b0\uff0c\u2234AC\u22a5BD\uff1b\uff083\uff09\u5982\u56fe5\uff0c\u8fc7\u70b9B\u4f5cBE\u2225CA\u4ea4DO\u4e8eE\uff0c\u2234\u2220BEO=\u2220ACO\uff0c\u53c8\u2235\u2220BOE=\u2220AOC\uff0c\u2234\u25b3BOE\u223d\u25b3AOC\uff0c\u2234 \uff0c\u53c8\u2235OB=kAO\uff0c\u7531\uff082\uff09\u7684\u65b9\u6cd5\u6613\u5f97BE=BD\uff0c\u2234 \u3002
\u89e3\uff1a\uff081\uff09\u76f4\u7ebfMN\u4e0e\u2299O\u7684\u4f4d\u7f6e\u5173\u7cfb\u662f\u76f8\u5207\u3002\u7406\u7531\u5982\u4e0b\uff1a\u8fde\u63a5OC\uff0c \u2235OA=OC\uff0c\u2234\u2220OAC=\u2220OCA\uff0c\u2235\u2220CAB=\u2220DAC\uff0c\u2234\u2220DAC=\u2220OCA\u3002\u2234OC\u2225AD\u3002\u2235AD\u22a5MN\uff0c\u2234OC\u22a5MN\u3002\u2235OC\u4e3a\u534a\u5f84\uff0c\u2234MN\u662f\u2299O\u5207\u7ebf\u3002\uff082\uff09\u2235CD=6\uff0c \uff0c\u2234AC=10\u3002\u7531\u52fe\u80a1\u5b9a\u7406\u5f97\uff1aAD=8\u3002\u2235AB\u662f\u2299O\u76f4\u5f84\uff0cAD\u22a5MN\uff0c\u2234\u2220ACB=\u2220ADC=90\u00b0\u3002\u2235\u2220DAC=\u2220BAC\uff0c\u2234\u25b3ADC\u223d\u25b3ACB\u3002\u2234 \uff0c\u5373 \u3002\u2234AB=12.5\u3002\u2234\u2299O\u534a\u5f84\u662f \u00d712.5=6.25\u3002 \u8bd5\u9898\u5206\u6790\uff1a\uff081\uff09\u8fde\u63a5OC\uff0c\u63a8\u51faAD\u2225OC\uff0c\u4ece\u800c\u5f97OC\u22a5MN\uff0c\u6839\u636e\u5207\u7ebf\u7684\u5224\u5b9a\u63a8\u51fa\u5373\u53ef\u3002\uff082\uff09\u6c42\u51faAD\u3001AB\u957f\uff0c\u8bc1\u25b3ADC\u223d\u25b3ACB\uff0c\u5f97\u51fa\u6bd4\u4f8b\u5f0f\uff0c\u4ee3\u5165\u6c42\u51faAB\u957f\u5373\u53ef\u3002
(1)AC=BD,BD⊥AC理由:∵∠AON=∠DOB,且∠ACN=∠BDN=45°
∴∠BOD=∠BDO=45°.
∴BD=BC.
∵AC=BC,
∴AC=BD.
∵∠BOD+∠BDO+∠B=180°,
∴∠B=90°,
∴BD⊥AC.
(2)AC=BD,BD⊥AC
理由:作AE⊥MN于E,BF⊥MN于F,延长AC交DB的延长线于点G,
∴∠AEC=∠BFO=∠BFD=90°.
∵∠ACN=∠GCM,且∠ACN=∠BDN=45°,
∴∠GCM=45°,
∴∠G=90°,
∴AC⊥DB.
在△AOE和△BOF中
绛旓細锛1锛堿C=BD锛孊D鈯C鐞嗙敱锛氣埖鈭燗ON=鈭燚OB锛屼笖鈭燗CN=鈭燘DN=45掳鈭粹垹BOD=鈭燘DO=45掳锛庘埓BD=BC锛庘埖AC=BC锛屸埓AC=BD锛庘埖鈭燘OD+鈭燘DO+鈭燘=180掳锛屸埓鈭燘=90掳锛屸埓BD鈯C锛庯紙2锛堿C=BD锛孊D鈯C鐞嗙敱锛氫綔AE鈯MN浜E锛孊F鈯N浜嶧锛屽欢闀緼C浜B鐨勫欢闀跨嚎浜庣偣G锛屸埓鈭燗EC=鈭燘FO=鈭燘FD=90掳锛庘埖... 绛旓細瑙o細锛1锛堿O = BD锛孉O鈯D锛涳紙2锛夎瘉鏄庯細濡傚浘4锛岃繃鐐笲浣淏E鈭A浜O浜嶦锛屸埓鈭燗CO = 鈭燘EO锛庡張鈭礎O = OB锛屸垹AOC = 鈭燘OE锛屸埓鈻矨OC 鈮 鈻矪OE锛庘埓AC = BE锛庡張鈭碘垹1 = 45掳锛 鈭粹垹ACO = 鈭燘EO = 135掳锛庘埓鈭燚EB = 45掳锛庘埖鈭2 = 45掳锛屸埓BE = BD锛屸垹EBD = 90掳锛庘埓AC =... 绛旓細鎵浠b鍨傜洿浜巃o 绛旓細濡傚浘 绛旓細鍋欱X骞宠浜嶢C浜MN浜X銆傝DXB=瑙1=45搴︺ 瑙2=45搴︺ 鎵浠ヨXBD=90搴︺ 鎵浠B鍨傜洿浜嶣D 鎵浠C鍨傜洿浜嶣D銆 ACO鍏ㄧ瓑浜嶺BO AC=XB 鍙堝洜涓 XB=BD锛堝洜涓45搴︼級 鎵鏈堿C=BD 绛旓細鎵浠ヨOFB涔熺瓑浜135搴 锛屾墍浠ヨDFB绛変簬45搴=瑙2 鎵浠ヨ竟BD=杈笲F 涓婇潰寰楀埌.AC=BF锛屾墍浠ユ湁AC=BD.寤堕暱AC浜B浜嶨,鍥犱负瑙1=45搴 瀵归《瑙掔殑鍏崇郴锛岃DCG=45搴 鍙堝洜涓鸿2绛変簬45搴 鎵浠ュ湪涓夎褰CG涓紝瑙扗GA=90搴 鍗矨C鈯D 锛3锛夊湪OD涓婂彇涓鐐 H 浣垮緱HB鍨傜洿浜嶣D 鍒欒DHB=45 鏄撶煡涓夎褰AC涓庝笁瑙... 绛旓細AC=BD涓擜C鈯D 璇佹槑锛濡傚浘锛杩囩偣B浣淏E鈭A浜O浜嶦锛屸埓鈭燗CO=鈭燘EO锛庡張鈭礎O=OB锛屸垹AOC=鈭燘OE锛屸埓鈻矨OC鈮屸柍BOE锛庘埓AC=BE锛庡張鈭碘垹1=45掳锛屸埓鈭燗CO=鈭燘EO=135掳锛庘埓鈭燚EB=45掳锛庘埖鈭2=45掳锛屸埓BE=BD锛屸垹EBD=90掳锛庘埓AC=BD锛庡欢闀緼C浜B鐨勫欢闀跨嚎浜嶧锛屽鍥撅紟鈭礏E鈭C锛屸埓鈭燗FD=90掳... 绛旓細闂殑鏄ab鍜BD鍚с傝BOD=瑙1=45掳 瑙払=180掳-瑙払OD-瑙2=90掳鎵浠ュ瀭鐩 绛旓細濡傚浘,鍦ㄥ钩闈㈢洿瑙掑潗鏍囩郴涓,鐩寸嚎mn鏄涓,涓夎薄闄愮殑瑙掑钩鍒嗙嚎,涓庣嚎娈礎B浜や簬C鐐,涓擜(2 0)B 5 04)1.姹備笁瑙掑舰ABO鐨勯潰绉2.鍦ㄧ洿绾縨n涓婃槸鍚﹀瓨鍦ㄧ偣P浣垮緱涓夎褰BP鐨勯潰绉槸涓夎褰BO闈㈢Н鐨2鍊嶃傝嫢瀛樺湪姹傜偣P鐨勫潗鏍囥傝嫢涓嶅瓨鍦ㄨ鏄庣悊鐢便3.鐐筈鏄涓夎薄闄愮洿绾縨n涓婁换鎰忎竴鐐,杩囩偣Q浣淨D鍨... 0 4)1.姹備笁瑙掑舰... 绛旓細锛1锛堿C = 3BD 锛孉C鈭D 锛庤瘉鈻矨OC鈭解柍BOD锛庯紙2锛堿C = BD 锛孉C鈯D 锛庤瘉锛氳繃鐐笲浣淏E鈭C浜O浜庣偣E锛屽欢闀緼C浜B鐨勫欢闀跨嚎浜庣偣F锛屸埖BE鈭C锛屸埓鈭燗FD = 90掳锛庘埓AC鈯D锛 本站交流只代表网友个人观点,与本站立场无关 |