MathDB
if A, P, Q are collinear, then AB = AC , two circles related

Source: INAMO Shortlist 2015 G5

May 14, 2019
geometrycirclescollineartangent

Problem Statement

Let ABCABC be an acute triangle. Suppose that circle Γ1\Gamma_1 has it's center on the side ACAC and is tangent to the sides ABAB and BCBC, and circle Γ2\Gamma_2 has it's center on the side ABAB and is tangent to the sides ACAC and BCBC. The circles Γ1\Gamma_1 and Γ2 \Gamma_2 intersect at two points PP and QQ. Show that if A,P,QA, P, Q are collinear, then AB=ACAB = AC.
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