Let ABC be a triangle and let L, M, N be the midpoints of the sides BC, CA and AB , respectively. The points P and Q lie on AB and BC, respectively; the points R and S are such that N is the midpoint of PR and L is the midpoint of QS. Show that if PS and QR are perpendicular, then their intersection lies on in the circumcircle of triangle LMN. geometryconcurrencyconcurrentcircumcircle