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For a triangle ABC, R = (5)/(2) and r = ...

For a triangle `ABC, R = (5)/(2) and r = 1`. Let D, E and F be the feet of the perpendiculars from incentre I to BC, CA and AB, respectively. Then the value of `((IA) (IB)(IC))/((ID)(IE)(IF))` is equal to _____

A

`(5)/(2)`

B

`(5)/(4)`

C

`(1)/(10)`

D

`(1)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
C

`rArr AI^(2) = (IE.IF)/(sin^(2)(A//2))`
`rArr (ID.IE.IF)/(IA.IB.IC) = sin.(A)/(2) sin.(B)/(2)sin.(C)/(2) = (r)/(4R) = (1)/(10)`
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