MathDB

In triangle

ABC

the medians

\overline{AD}

and

\overline{CE}

have lengths 18 and 27, respectively, and AB \equal{} 24. Extend

\overline{CE}

to intersect the circumcircle of

ABC

F

. The area of triangle

AFB

m\sqrt {n}

, where

m

and

n

are positive integers and

n

is not divisible by the square of any prime. Find m \plus{} n.

Problem Statement