Question 127
Point $P$ is chosen inside isosceles triangle $ABC$ with base $BC$ and $\angle BAC \lt 90^\circ$ in such a way, that $\angle BPC = 2\angle BAC$. Let $K$ be the feet of perpendicular from $A$ to the line which contains the bisector of adjacent angle of $\angle BPC$. Prove, that $BP + PC = 2AK$.