Question 13
Let $P$ be an interior point of acute triangle $ABC$ such that $CP=BP$ and $\angle BPC=2\angle BAC$. Let the angle bisector of $\angle ACB$ and $AB$ intersect at $L$ and point $H$ be on $AB$ such that $CH\perp AB$, where $L$ is between points $A$ and $H$, as shown in the diagram below. If $CP=CH=28$ cm and the area of triangle $CPL$ is $196$ cm$^2$, then find the length, in cm, of $LH$.
Show your detailed solution.
Show your detailed solution.