题目内容
如图,⊙
的半径为2,
,
切⊙
于
,弦
,连结
,图中阴影部分的面积为 .
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试题分析:连接OB、OC,根据切线的性质可得∠ABO=90°,再由OB=2,
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连接OB、OC
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∵
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∴∠ABO=90°
∵OB=2,

∴∠BAO=30°
∴∠AOB=60°
∵

∴△OBC的面积等于△ABC的面积,∠OBC=60°
∵OB=OC
∴∠COB=60°
∴阴影部分的面积

点评:解题的关键是读懂题意及图形,正确作出辅助线,把阴影部分的面积转化为扇形的面积.
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