如图,AB=AC,OB=OC,AD切圆o于D.求证:AC与圆o相切

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如图,AB=AC,OB=OC,AD切圆o于D.求证:AC与圆o相切
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如图,AB=AC,OB=OC,AD切圆o于D.求证:AC与圆o相切
如图,AB=AC,OB=OC,AD切圆o于D.求证:AC与圆o相切

如图,AB=AC,OB=OC,AD切圆o于D.求证:AC与圆o相切
连接OD,过C作OE⊥AC于E,
∵AB是切线,∴OD⊥AB,
∵AB=AC,∴∠B=∠C,
∵OB=OC,∠BDO=∠CEO=90°,
∴ΔOBD≌ΔOCE,
∴OE=OD,
∴AC是圆O的切线.