A difficult geometry from Iranian TST 2017
Source: Iranian TST 2017, first exam day 2, problem 5
April 6, 2017
geometryIranIranian TSTcircumcircle
Problem Statement
In triangle , arbitrary points lie on side such that and lies between .The circumcircle of triangle intersects sides at respectively.The point is the intersection of .Two lines passing through the midpoint of and parallel to and , intersect and at points respectively.
Prove that the circumcircle of triangle and triangle are tangent to each other.Proposed by Iman Maghsoudi