Let P be an interior point of a circle Γ centered at O where P≠O. Let A and B be distinct points on Γ. Lines AP and BP meet Γ again at C and D, respectively. Let S be any interior point on line segment PC. The circumcircle of △ABS intersects line segment PD at T. The line through S perpendicular to AC intersects Γ at U and V . The line through T perpendicular to BD intersects Γ at X and Y . Let M and N be the midpoints of UV and XY , respectively. Let AM and BN meet at Q. Suppose that AB is not parallel to CD. Show that P,Q, and O are collinear if and only if S is the midpoint of PC.