MathDB
Point of concurrency independent of incircle

Source: Czech-Polish-Slovak Match, 2009

August 20, 2011
geometry

Problem Statement

Let ω\omega denote the excircle tangent to side BCBC of triangle ABCABC. A line ℓ\ell parallel to BCBC meets sides ABAB and ACAC at points DD and EE, respectively. Let ω′\omega' denote the incircle of triangle ADEADE. The tangent from DD to ω\omega (different from line ABAB) and the tangent from EE to ω\omega (different from line ACAC) meet at point PP. The tangent from BB to ω′\omega' (different from line ABAB) and the tangent from CC to ω′\omega' (different from line ACAC) meet at point QQ. Prove that, independent of the choice of ℓ\ell, there is a fixed point that line PQPQ always passes through.
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