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Question

In ΔABC, cotA2+cotB2+cotC2 is equal to

A
Δr2
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B
(a+b+c)2abc2R
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C
Δr
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D
ΔRr
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Solution

The correct option is A Δr2
cotA2+cotB2+cotC2
=s(sa)(sb)(sc)+s(sb)(sa)(sc)+s(sc)(sb)(sa)
=(sa)s(sa)(sb)(sc)+(sb)s(sa)(sb)(sc)+(sc)s(sb)(sa)(sc)
=s(sa)(sb)(sc)(3s2s)
=s2Δ
=Δr2 (r=Δs)

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