In $△ A B C,$ right angled at $A$ , what is the value of $r + R$ ?

\frac{a + c}{2}

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b + c

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\frac{b + c}{2}

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\frac{a + b + c}{2}

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Solution

The correct option is D $\frac{b + c}{2}$
$2 R = \frac{a}{sin A} ⟹ 2 R = a$
$r = (s - a) tan \frac{A}{2} ⟹ r = \frac{a + b + c}{2} - a ⟹ 2 r = b + c - a$

$∴ R + r = \frac{a + b + c - a}{2} = \frac{b + c}{2}$

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