Consider a triangle ABC and | Maths | JEE ADVANCED 2010

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Consider a triangle ABC and let $\mathrm{a}, \mathrm{b}$ and c denote the lengths of the sides opposite to vertices $\mathrm{A}, \mathrm{B}$ and C respectively. Suppose $\mathrm{a}=6, \mathrm{~b}=10$ and the area of the triangle is $15 \sqrt{3}$. If $\angle \mathrm{ACB}$ is obtuse and if r denotes the radius of the incircle of the triangle, then $r^2$ is equal to

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