Let ABC be a triangle. Its incircle meets the sides BC,CA and AB in the points D,E and F, respectively. Let P denote the intersection point of ED and the line perpendicular to EF and passing through F, and similarly let Q denote the intersection point of EF and the line perpendicular to ED and passing through D.
Prove that B is the mid-point of the segment PQ.Proposed by Karl Czakler geometrymidpointincircleperpendicular