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Three circles and a chord

Source: 239 2008 J6

July 28, 2020
geometry

Problem Statement

ABAB is the chord of the circle SS. Circles S1S_1 and S2S_2 touch the circle SS at points PP and QQ, respectively, and the segment ABAB at point KK. It turned out that ∠PBA=∠QBA\angle{PBA}=\angle{QBA}. Prove that ABAB is the diameter of the circle SS.
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