Thread: Bisector

The bisector of angle of the triangle meets the opposite side at a point If and are the respective feet from to and from to , prove that the points and are harmonic.

Originally Posted by yusukered07

The bisector of angle of the triangle meets the opposite side at a point If and are the respective feet from to and from to , prove that the points and are harmonic.

Triangle BPQ and CPR are similar.
So PQ/PR = BQ/CR.
Similarly triangle ABQ and ACR are similar.
So BQ/RC = AQ/AR.
Combine the two equations and see what you get.