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Q.

For triangle ABC, R = 5/2 and r = 1. Let l be the incentre of the triangle and D, E and F be the feet of the  perpendiculars from I to BC, CA and AB, respectively. The value of ID×IE×IFIA×IB×IC is equal to

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a

1/10

b

5/2

c

1/5

d

5/4

answer is C.

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Detailed Solution

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In triangles AIF and AlE
IFsin(A/2)=AI=IEsin(A/2) AI2=IEIFsin2(A/2)IDIEIFIAIBIC=sinA2sinB2sinC2=r4R=110

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