Let ABCD be a quadrilateral and P a point in the plane of the quadrilateral. Let M,N be on the sides AC,BD respectively such that PM∥BC,PN∥AD. AC meets BD at E. Prove that the orthocenter of triangles EBC,EAD,EMN are collinear if and only if P is on the line AB.Đỗ Thanh SơnPS. Instead of the word collinear, it was written concurrent, probably a typo. geometryorthocentercollinear