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Question

In any triangle ABC;a2+b2+c2R2 has the maximum value

A
3
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B
6
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C
9
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D
None of these
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Solution

The correct option is C 9
In triangle ABC;a2+b2+c2R2=4[sin2A+sin2B+sin2C]

=4[3cos2Acos2Bcos2C]

=4[3cos2A+12cos2B+12cos2C+12]

=4[3212(cos2A+cos2B+cos2C)]

=4[3212(cos2A+cos2B+cos2C)]

=8[1+cosAcosBcosC]8[1+18]=9

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