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In any triangle A B C ,(a^2+b^2+c^2)/(R^...

In any triangle `A B C ,(a^2+b^2+c^2)/(R^2)` has the maximum value of (a) 3 (b) 6 (c) 9 (d) none of these

A

3

B

6

C

9

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
In triangle ABC,
`(a^(2) + b^(2) + c^(2))/(R^(2)) = 4(sin^(2) A + sin^(2) B + sin^(2) C)`
`= 8(1 + cos A cos B cos C) le 8(1 + (1)/(8)) le 9`
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CENGAGE-PROPERTIES AND SOLUTIONS OF TRIANGLE-Exercise (Single)
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  14. In a right-angled isosceles triangle, the ratio of the circumradius an...

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  17. In triangle A B C , let /c=pi/2dot If r is the inradius and R is circu...

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