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In a right angle triangle $ABC$ with vertex $B$ being the right angle, the mutually perpendicular sides $AB$ and $BC$ are $p$ cm. and $q$ cm. long respectively. If the length of hypotenuse is $\left ( p+q-6 \right )$ cm., then the radius of the largest possible circle that can be inscribe in the triangle is ____________

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$(a-r) + (b-r) = 2R$

$\Rightarrow (p-r) + (q-r) = p+q-6$ ( given a=p, b=q, 2R = p+q-6)

$\Rightarrow p+q-2r = p+q-6$

$\Rightarrow 2r = 6$

$\Rightarrow r = 3$

$\therefore r = 3 cm$

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