Problem

Source: Taiwan 2014 TST3, Problem 3

Tags: geometry, circumcircle, incenter, geometric transformation, homothety, ratio, parallelogram



Let M be any point on the circumcircle of triangle ABC. Suppose the tangents from M to the incircle meet BC at two points X1 and X2. Prove that the circumcircle of triangle MX1X2 intersects the circumcircle of ABC again at the tangency point of the A-mixtilinear incircle.