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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)`c+a` (d) `a+b+c`

Text Solution

Verified by Experts

Here, `C = pi/2`
Now, `c = 2RsinC = 2R`
`=>R = c/2`
`=>2R = c->(1)`
`r = (s-c)tan(C/2) = (s-c)tan(pi/4)`
`=>r = s-c`
`=>2r = 2s-2c = a+b+c-2c = a+b-c`
From (1),
...
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