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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+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
Here, `R^(2)=MC^(2)=1/4(a^(2)+b^(2)) " "["by distance from origin"]`
`=1/4c^(2)" "["by Pythagoras theorem"]`

`rArr" "R=c/2`
Next, `r=(s-c)tan(C//2)=(s-c)tanpi//4=s-c`
`:." "2(r+R)=2r+2R=2s-2c+c`
=a+b+c-c
= a + b
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