Four Collinear Points Related to the Altitudes
Let ABC be a triangle. Let A', B', and C' be the feet of the altitudes from A, B, and C. Let P and Q be the projections of A' to AB and AC. Let R and S be the projections of A' to BB' and CC'. Then P, Q, R, and S are collinear.
See problem 5 in N. Altshiller-Court, College Geometry, Mineola, NY: Dover, 2007 p. 99.