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Question

If r1,r2, and r3 be the radii of encircles ABC, then r1r1r2is equal to:

A
cotA2
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B
cotA2cotB2
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C
tanA2
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D
tanA2
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Solution

The correct option is C tanA2
Since,
r1+r2+r3r1r2+r2r3+r3r1=Δsa+Δsb+ΔscΔ1(sa)(sb)+1(sb)(sc)+1(sc)(sa)=1sa+1sb+1sc(sc)+(sa)+(sb)(sa)(sb)(sc)=1sa+1sb+1scsΔ=Δsa+Δsb+Δscs=Δs(sa)+Δs(sb)+Δs(sc)=tanA2+tanB2+tanC2=tanA2

Hence, the option C is the correct answer.

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