MathDB
Two circles and concyclic points

Source: Mexican Quarantine Mathematical Olympiad P3

April 25, 2020
geometryConcyclictangent

Problem Statement

Let Γ1\Gamma_1 and Γ2\Gamma_2 be circles intersecting at points AA and BB. A line through AA intersects Γ1\Gamma_1 and Γ2\Gamma_2 at CC and DD respectively. Let PP be the intersection of the lines tangent to Γ1\Gamma_1 at AA and CC, and let QQ be the intersection of the lines tangent to Γ2\Gamma_2 at AA and DD. Let XX be the second intersection point of the circumcircles of BCPBCP and BDQBDQ, and let YY be the intersection of lines ABAB and PQPQ. Prove that CC, DD, XX and YY are concyclic.
Proposed by Ariel García
Back to ProblemsView on AoPS