MathDB

6

Part of 2018 Romanian Master of Mathematics

Problems(1)

Geometry with fix circle

Source: RMM 2018 Problem 6

2/25/2018
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.
geometryRMM 2018