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Question

In ΔABC, ratio of area of incircle to area of ΔABC=

A
π : Tan A2 Tan B2 Tan C2
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B
π : Cot A2 Cot B2 Cot C2
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C
1:1
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D
π:r
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Solution

The correct option is A π : Cot A2 Cot B2 Cot C2
r=(sa)tanA/2=(sb)tanB/2=(sc)tanC/2=Sr3(sa)(sb)(sc)=tanA2tanB2tanC2r3.ss(sa)(sb)(sc)=tanA2tanB2tanC2r3.s2=tanA2tanB2tanC2r2=tanA2tanB2tanC2
πr2=π×tanA2tanB2tanC2πr2=π:cotA2cotB2cotC2

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