一首好的曲子,使人有余音不绝之感,一道好的习题,探寻起来,其“余韵”也足以让人叹咏回味。去年十二月江苏省举办的第十届初中数学竞赛中,便有这样的好题。原题是: 如图一,已知AB、BC、CD分别与圆相切于E、F、G,AB=BC=CD,连结AC与BD相交于P,连结PF,求证:PF⊥BC 简证 连PO、FO,连BO、CO并延长分别交BD、AC于J,K;连EO、GO延长分别 A good tune makes people feel reverberant, a good exercise, and a search for it. Its “Ring” is enough to make people sigh. In the 10th junior high school math competition held in Jiangsu Province last December, there were such good questions. The original question is: As shown in Figure 1, AB, BC, and CD are known to be tangential to the circle at E, F, G, and AB=BC=CD, respectively, and the AC and BD intersect at P, linking PF. Proof: PF ⊥ BC Connect PO, FO, even BO, CO and extend BD, AC to J, K respectively; even EO, GO extend respectively