MathDB
2 symmetrical (to the circumcircle) circles are tangent iff a triangle is right

Source: Sharygin 2010 Final 9.7

October 6, 2018
geometrytangent circlesright trianglesymmetry

Problem Statement

Given triangle ABCABC. Lines ALaAL_a and AMaAM_a are the internal and the external bisectrix of angle AA. Let ωa\omega_a be the reflection of the circumcircle of △ALaMa\triangle AL_aM_a in the midpoint of BCBC. Circle ωb\omega_b is defined similarly. Prove that ωa\omega_a and ωb\omega_b touch if and only if △ABC\triangle ABC is right-angled.
Back to ProblemsView on AoPS