Question 76
Let $ABC$ be a triangle with the angle $\angle BAC = 30^\circ$, and let $P$ be an arbitrary point inside this triangle. Denote the mirror images of the point $P$ with respect to the sides $BC$, $CA$, and $AB$ by $P_A$, $P_B$, and $P_C$, respectively. Let $P_A P_B P_C$ be an equilateral triangle. Prove that $\angle BPC = 90^\circ$.