Question

（8分）如圖，在△ABC中，AB=AC，點(diǎn)O為底邊上的中點(diǎn)，以點(diǎn)O為圓心，
1為半徑的半圓與邊AB相切于點(diǎn)D．
（1）判斷直線AC與⊙O的位置關(guān)系，并說明理由；
（2）當(dāng)∠A＝60°時(shí)，求圖中陰影部分的面積．

Answer 1

解：（1）直線AC與⊙O相切．························································· 1分
理由是：
連接OD,過點(diǎn)O作OE⊥AC，垂足為點(diǎn)E．

∵⊙O與邊AB相切于點(diǎn)D，
∴OD⊥AB．·························································································· 2分
∵AB=AC，點(diǎn)O為底邊上的中點(diǎn)，
∴AO平分∠BAC····················································································· 3分
又∵OD⊥AB，OE⊥AC
∴OD= OE····························································································· 4分
∴OE是⊙O的半徑．
又∵OE⊥AC，∴直線AC與⊙O相切．·························································· 5分
（2）∵AO平分∠BAC，且∠BAC=60°，∴∠OAD=∠OAE=30°，
∴∠AOD=∠AOE=60°，

解析