# Math Help - Bisector

1. ## Bisector

The bisector of angle $A$ of the triangle $ABC$ meets the opposite side at a point $P.$ If $Q$ and $R$ are the respective feet from $B$ to $AP$ and from $C$ to $AP$, prove that the points $A,P,Q$and $R$ are harmonic.

2. Originally Posted by yusukered07
The bisector of angle $A$ of the triangle $ABC$ meets the opposite side at a point $P.$ If $Q$ and $R$ are the respective feet from $B$ to $AP$ and from $C$ to $AP$, prove that the points $A,P,Q$and $R$ 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.