In triangle ABC, let `angle C = pi//2`. If r is the inradius and R is circumradius of the triangle, then `2(r + R)` is equal to

Monjur Alahi

In triangle ABC, let `angle C = pi//2`. If r is the inradius and R is circumradius of the triangle, then `2(r + R)` is equal to
A. `a + b`
B. `b + c`
C. `c + a`
D. `a + b + c`


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Correct Answer - A
Since `DeltaABC` is right angled at C, circum-radius, `R = (c)/(2)`
Now, `r = (s -c) tan (C//2) = (s-c) tan (pi//4) = s -c`
Thus, `2(r +R) = 2r + 2R = 2s -c = a + b`

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