Let ABC be a triangle right-angled at B. If a | vedclass

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(D) In a right-angled triangle $ABC$ at $B$, the sides are $a$ (opposite to $A$), $c$ (opposite to $C$), and $b$ (hypotenuse opposite to $B$).Given $a

Vedclass · Accepted Answer

$48.5$

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(D) In a right-angled triangle $ABC$ at $B$, the sides are $a$ (opposite to $A$), $c$ (opposite to $C$), and $b$ (hypotenuse opposite to $B$).Given $a = 13$ and $c = 84$.The hypotenuse $b = \sqrt{a^2 + c^2} = \sqrt{13^2 + 84^2} = \sqrt{169 + 7056} = \sqrt{7225} = 85$.The inradius $r$ of a right-angled triangle is given by $r = \frac{a + c - b}{2} = \frac{13 + 84 - 85}{2} = \frac{12}{2} = 6$.The circumradius $R$ of a right-angled triangle is half the hypotenuse, so $R = \frac{b}{2} = \frac{85}{2} = 42.5$.Therefore, $r + R = 6 + 42.5 = 48.5$.

Let $ABC$ be a triangle right-angled at $B$. If $a = 13$ and $c = 84$, then $r + R = $

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