Consider a triangle `A B C` and let `a , ba n dc` denote the lengths of the sides opposite to vertices `A , B ,a n dC` , respectively. Suppose `a=6,b=10 ,` and the area of triangle is `15sqrt(3)dot` If `/_A C B` is obtuse and if `r` denotes the radius of the incircle of the triangle, then the value of `r^2` is

Explanation

To solve the problem, we will follow these steps:

### Step 1: Use the area formula to find \( \sin C \)

The area \( \Delta \) of triangle \( ABC \) can be expressed using the formula:
\[ \Delta = \frac{1}{2}ab \sin C \]
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