MathDB
Problem 1, BMO 2020

Source: Problem 1, BMO 2020

November 1, 2020
geometryBMO

Problem Statement

Let ABCABC be an acute triangle with AB=ACAB=AC, let DD be the midpoint of the side ACAC, and let γ\gamma be the circumcircle of the triangle ABDABD. The tangent of γ\gamma at AA crosses the line BCBC at EE. Let OO be the circumcenter of the triangle ABEABE. Prove that midpoint of the segment AOAO lies on γ\gamma.
Proposed by Sam Bealing, United Kingdom
Back to ProblemsView on AoPS