Question 83
Let ABC be a triangle. Take D∈[AC], E∈[AB] with BE=CD. Let P=BD∩CE. The circumcircles of BEP and CDP meet again at Q. Let K,L be the midpoints of BE,CD respectively. Let R be the intersection of the perpendicular to QK at K and the perpendicular to QL at L. Prove:
1) R lies on the circumcircle of ABC;
2) Q lies on the bisector of angle BAC.
1) R lies on the circumcircle of ABC;
2) Q lies on the bisector of angle BAC.