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Singapore TST 2009 Day 1 Problem 1

Source:

August 2, 2010
geometrygeometric transformationhomothetysearchfunctioncircumcirclepower of a point

Problem Statement

Two circles are tangent to each other internally at a point  T\ T . Let the chord  AB\ AB of the larger circle be tangent to the smaller circle at a point  P\ P . Prove that the line  TP\ TP bisects  ∠ATB\ \angle ATB .
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