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symmedian in two circles

Source: Iran second round- 2013- P4

May 4, 2013
geometrycircumcirclegeometric transformationreflectiongeometry proposed

Problem Statement

Let PP be a point out of circle CC. Let PAPA and PBPB be the tangents to the circle drawn from CC. Choose a point KK on ABAB . Suppose that the circumcircle of triangle PBKPBK intersects CC again at TT. Let P′{P}' be the reflection of PP with respect to AA. Prove that ∠PBT=∠P′KA \angle PBT = \angle {P}'KA
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