ToT 2021-spring JA3

There is an equilateral triangle $ABC$ . Let $E, F$ and $K$ be points such that $E{}$ lies on side $AB$ , $F{}$ lies on the side $AC$ , $K{}$ lies on the extension of side $AB$ and $AE = CF = BK$ . Let $P{}$ be the midpoint of the segment $EF$ . Prove that the angle $KPC$ is right.

Vladimir Rastorguev