MathDB

15

Part of 2022 Baltic Way

Problems(1)

XY is tangent to a fixed circle

Source: Baltic Way 2022/15

11/12/2022
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.
geometry