Consider a triangle \( \mathrm{ABC} \) and let \( \mathrm{a}, \math...

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Consider a triangle \( \mathrm{ABC} \) and let \( \mathrm{a}, \mathrm{b} \) and \( \mathrm{c} \) denote the lengths of the sides opposite to vertices \( \mathrm{A}, \mathrm{B} \) and
P \( C \) respectively. Suppose \( a=6, b=10 \) and the area of the triangle is \( 15 \sqrt{3} \). If \( \angle A C B \) is obtuse and if \( r \)

W denotes the radius of the incircle of the triangle, then \( \mathrm{r}^{2} \) is equal to
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