MathDB
Geometry with fix circle

Source: RMM 2018 Problem 6

February 25, 2018
geometryRMM 2018

Problem Statement

Fix a circle Γ\Gamma, a line ℓ\ell to tangent Γ\Gamma, and another circle Ω\Omega disjoint from ℓ\ell such that Γ\Gamma and Ω\Omega lie on opposite sides of ℓ\ell. The tangents to Γ\Gamma from a variable point XX on Ω\Omega meet ℓ\ell at YY and ZZ. Prove that, as XX varies over Ω\Omega, the circumcircle of XYZXYZ is tangent to two fixed circles.
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