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XY is tangent to a fixed circle

Source: Baltic Way 2022/15

November 12, 2022
geometry

Problem Statement

Let Ω\Omega be a circle, and B,CB, C are two fixed points on Ω\Omega. Given a third point AA on Ω\Omega, let XX and YY denote the feet of the altitudes from BB and CC, respectively, in the triangle ABCABC. Prove that there exists a fixed circle Γ\Gamma such that XYXY is tangent to Γ\Gamma regardless of the choice of the point AA.
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