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In a triangle ABC, let $C = \frac{π}{2},$ if $r$ is the in radius and R is circum radius of the triangle then $2 (r + R)$ is equal to

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$a + b$

$b + c$

$c + a$

$a + b + c$

answer is A.

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Detailed Solution

$C = 90^{0} \Rightarrow R = \frac{c}{2} A n d r = (S - c) \tan (\frac{C}{2}) = S - c a n d 2 (r + R) = 2 S - 2 c + c = a + b$

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