Problem

Consider a

\Delta ABC

and let

a, b

and

c

denote the lengths of the sides opposite to vertices

A, B

and

C

, respectively.

a = 6, b = 10

and the area of the triangle is

15\sqrt{3}

. If

\angle ACB

is obtuse and if

r

denotes the radius of the incircle of the triangle, then

r^2

is equal to.....