The side of a triangle are $5, 12, 13$ . The area of triangle formed by its centroid ‘ $G$ ’ circum center ‘ $S$ ’ and in center $I$ is $\frac{a}{b}$ then $a + b$ is

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answer is 13.

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Detailed Solution

$5^{2} + 12^{2} = 13^{2} \to C$
The triangle is right angle triangle such that
$G = (4, \frac{5}{3}); S = (6, \frac{5}{2})$
$I = (2, 2) \to area of the triangle GSI = \frac{7}{6}$

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