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In triangle A B C , let /c=pi/2dot If r ...

In triangle `A B C ,` let `/_c=pi/2dot` 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+a` (d) `a+b+c`

A

`a + b`

B

`b + c`

C

`c + a`

D

`a + b + c`

Text Solution

Verified by Experts

The correct Answer is:
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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