ITOT 42 Spring 2021 - THCS A - additive practice Question 3

In equilateral triangle $ABC$, point $E$ lies on $AB$, point $F$ on $AC$, and point $K$ on the line $AB$ outside segment $AB$, with $AE=CF=BK$. Let $P$ be the midpoint of $EF$. Prove that $\angle KPC$ is a right angle. (6 points)