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第74頁

信息發(fā)布者：
?$證明：連接CD$?
?$可得：∠B=∠D$?
?$∵AD為直徑$?
?$∴∠ACD為直角$?
?$∴∠ACE +∠DCE=90$?
?$∵CE⊥AD$?
?$∴∠D+∠DCE =90°$?
?$∴∠ACF =∠D$?
?$∴∠ACF=∠ABC$?
?$ 解：過點O作OE⊥AC于點E$?
?$∵∠AOB=90°，AO=5，OB=12$?
?$∴AB=13$?
?$∴EO×AB=AO×BO$?
?$∴ EO=\frac {AO×BO}{AB}=\frac {60}{13}$?
?$在Rt△AEO中， AE=\sqrt{AO^2-EO^2}=\frac {25}{13}$?
?$∴ AC=\frac {25}{13}×2=\frac {50}{13}$?
?$∴ BC=13-\frac {50}{13}=\frac {119}{13}$?

?$解：連接AD$?
?$∵AO= DO$?
?$∴ ∠A=\frac 12(180° - 70°) = 55°$?
?$∵AB是圓O的直徑$?
?$∴∠ADB=90°$?
?$∴∠B= 35°$?
?$∵OD=OB$?
?$∴∠ODB=∠B=35°$?
?$∴∠ODP =∠AOD -∠OPD= 10°$?
?$∴∠BDC=25°$?
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