Question 59
The triangle $ABC$ is isosceles with $AB = AC$. The point $P$ inside $ABC$ satisfies two conditions:
(i) $A$ lies on the trisector line of $\angle BPC$, i.e. $AP$ meets $BC$ at $Q$ such that $\angle BPC = 3 \angle QPC$;
(ii) $\angle BPQ = \angle BAC$.
Show that $Q$ trisects $BC$, i.e. $BC = 3 \cdot QC$.
(i) $A$ lies on the trisector line of $\angle BPC$, i.e. $AP$ meets $BC$ at $Q$ such that $\angle BPC = 3 \angle QPC$;
(ii) $\angle BPQ = \angle BAC$.
Show that $Q$ trisects $BC$, i.e. $BC = 3 \cdot QC$.