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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 _____

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The correct Answer is:
10
`((IA)(IB)(IC))/((ID)(IE)(IF)) = ((r "cosec"(A)/(2)) (r "cosec"(B)/(2)) (r "cosec"(C)/(2)))/(r^(3))`
`= (1)/("sin"(A)/(2) "sin"(B)/(2) "sin"(C)/(2)) = (4R)/(r) = 10`
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