An ellipse Γ1 with foci at the midpoints of sides AB and AC of a triangle ABC passes through A, and an ellipse Γ2 with foci at the midpoints of AC and BC passes through C. Prove that the common points of these ellipses and the orthocenter of triangle ABC are collinear. geometryellipsede longchamps pointcollinearitySharygin Geometry OlympiadSharygin 2023