In $\triangle ABC$, $AB=18, AC=24$ and $BC=30$. Point P is on side $AB$ and a line is drawn through $P$so that half of the perimeter of ABC lies on each side of the line and half of the area of ABC lies on each side of the line. What is the square of the distance CP?
I’ve tried scaling it down to a 3,4,5 triangle, a right triangle. Then each side must add up to 6 with area of 3. This is where I’m stuck. I don’t know if I did anything wrong. Someone please help me.
