(GKH) and (ABC) are tangent
Source: Kvant M2793
July 10, 2024
geometrycircumcircleparallelogramtangent circles
Problem Statement
In acute triangle () point is center of its circumcircle . Let the tangent to drawn at point intersect the line at point . Let the line intersects the segments and at points and , respectively. Point is constructed such that is a parallelogram. Let and be points of intersection of segment with segments and , respectively. Prove that the circle touches the circle .
Proposed by Dong Luu