Question 30
A triangle, $\triangle ABC$, has sides $AB=18$, $AC=24$, and $BC=30$. Point $P$ is on side $AB$ and a line is drawn through $P$ so that half of the perimeter of $\triangle ABC$ lies on each side of the line and half of the area of $\triangle ABC$ lies on each side of the line. What is the square of the distance $CP$?