MathNet 2022-part-01 — 197 problems (EN–VI) Question 139

In an acute triangle $ABC$, point $M$ is the midpoint of $AB$ and $AH$ is the altitude. Let $CP$ be the perpendicular to the line $MH$. If $AB = 21$, $BH = 7$ and $BP = CP$, find the length of $AC$.