如图,圆O1O2是等圆,点P是圆O1O2的中心,过点P作直线AD交圆O1于点AB交圆O2于点CD求证AB=CD

分别过O1,O2作O1E⊥AB,O2F⊥CD,连接O1A,O2D∵∠O1EP=∠O2FP=90°,∠O1PE=∠O2PF,O1P=O2P∴△O1PE≌△O2PF∴O1E=O2F∵O1A=O2D  （等圆）∴RT△O1AE≌RT△O2DF  （HL）∴AE=DF∵AB=2AE,CD=2DF （垂径定理）∴AB=CD