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BxMO 2015, Problem 2

Source: Benelux Mathematical Olympiad 2015, Problem 2

May 10, 2015
geometrycircumcircle

Problem Statement

Let ABCABC be an acute triangle with circumcentre OO. Let ΓB\mathit{\Gamma}_B be the circle through AA and BB that is tangent to ACAC, and let ΓC\mathit{\Gamma}_C be the circle through AA and CC that is tangent to ABAB. An arbitrary line through AA intersects ΓB\mathit{\Gamma}_B again in XX and ΓC\mathit{\Gamma}_C again in YY. Prove that ∣OX∣=∣OY∣|OX|=|OY|.
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