Tangent circles
Source: 239 2019 S5
July 31, 2020
geometry
Problem Statement
Circle touches the circumcircle of triangle at point , and it touches the sides and at points and , respectively. Rays and intersect at point . The tangent line at point to the circle meets the segment at point . The line segment intersects the circumcircle of triangle at point . Prove that the circumscribed circles of triangles and are tangent.