MathDB
BMO Shortlist 2021 G5

Source: BMO Shortlist 2021

May 8, 2022
Balkanshortlist2021geometryreflectionparallel

Problem Statement

Let ABCABC be an acute triangle with AC>ABAC > AB and circumcircle Γ\Gamma. The tangent from AA to Γ\Gamma intersects BCBC at TT. Let MM be the midpoint of BCBC and let RR be the reflection of AA in BB. Let SS be a point so that SABTSABT is a parallelogram and finally let PP be a point on line SBSB such that MPMP is parallel to ABAB. Given that PP lies on Γ\Gamma, prove that the circumcircle of △STR\triangle STR is tangent to line ACAC.
Proposed by Sam Bealing, United Kingdom
Back to ProblemsView on AoPS