# Triplication

Geometry Level 4

In $$\triangle ABC$$, $$AC = 4$$, $$BC = 5$$, and $$AB = 6$$, point $$E$$ is on $$\overline{AB}$$ so that $$AE$$ = $$\dfrac{1}{2}EB$$.

If the sums of $$CE$$ and the measure of the segment from $$E$$ to the midpoint of $$\overline{CB}$$ can be written as: $\frac{1}{2}\sqrt{P+Q\sqrt{R}},$ where $$P,Q,R$$ are all integers. Find $$P$$.

×