Let I be the incenter of a right-angled triangle ABC, and M be the midpoint of hypothenuse AB. The tangent to the circumcircle of ABC at C meets the line passing through I and parallel to AB at point P. Let H be the orthocenter of triangle PAB. Prove that lines CH and PM meet at the incircle of triangle ABC.
concurrentgeometryconcurrenctright trianglegeometry solvedsimilar triangleshumpty points