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