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In a right-angled isosceles triangle, th...

In a right-angled isosceles triangle, the ratio of the circumradius and inradius is `2(sqrt(2)+1):1` (b) `(sqrt(2)+1):1` `2:1` (d) `sqrt(2):1`

A

`2(sqrt2 + 1) : 1`

B

`(sqrt2 + 1): 1`

C

`2 : 1`

D

`sqrt2 : 1`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `R = (sqrt2a)/(2) = (a)/(sqrt2)`
`r = (Delta)/(s) = ((1)/(2)a^(2))/((1)/(2) (a + a + sqrt2a)) = (a)/(2+ sqrt2)`
`:. (R)/(r) = (a)/(sqrt2) xx (2 + sqrt2)/(a) = sqrt2 + 1`
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