Y by Aref, rashah76, samrocksnature, Adventure10, jhu08, mathematicsy, MathLuis, Mango247
Let be a triangle, and the midpoint of its side . Let be the incircle of triangle . The median of triangle intersects the incircle at two points and . Let the lines passing through and , parallel to , intersect the incircle again in two points and . Let the lines and intersect again at the points and . Prove that .