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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 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 PUBLICATION-PROPERTIES AND SOLUTIONS OF TRIANGLE-Exercises
  1. If 8R^2=a^2+b^2+c^2 then show that the triangle is right angled

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  2. Let ABC be a triangle with /A=45^0dot Let P be a point on side BC with...

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  3. In any triangle A B C ,(a^2+b^2+c^2)/(R^2) has the maximum value of 3 ...

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  4. In triangle A B C ,R(b+c)=asqrt(b c),w h e r eR is the circumradius of...

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  5. In A B C , if b^2+c^2=2a^2, then value of (cotA)/(cotB+cotC) is

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  6. If sinthetaa n d-costheta are the roots of the equation a x^2-b x-c=0 ...

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  7. If D is the mid-point of the side B C of triangle A B C and A D is per...

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  8. In a triangle ABC, if cotA :cotB :cotC = 30: 19 : 6 then the sides a, ...

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  9. In A B C ,P is an interior point such that /P A B=10^0/P B A=20^0,/P ...

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  10. In A B C , if A B=c is fixed, and cosA+cosB+2cos C=2 then the locus o...

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  11. If in A B C ,A=pi/7,B=(2pi)/7,C=(4pi)/7 then a^2+b^2+c^2 must be (a)R...

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  12. In Delta ABC, "cot"(A)/(2) + "cot" (B)/(2) + "cot" (C)/(2) is equal to

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  13. In A B C ,(cot (A/2)+cot(B/2))(asin^2(B/2)+bsin^2(A/2))= (a) cotC (...

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  14. In a right-angled isosceles triangle, the ratio of the circumradius an...

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  15. In a ΔABC, a semicircle is inscribed, whose diameter lies on the side ...

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  16. In A B C ,A(2pi)/3,b-c=3sqrt(3)c m and area of A B C=(9sqrt(3))/2c m...

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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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  18. In the given figure A B is the diameter of the circle, centred at Odot...

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  19. In triangle A B C ,ifPdotQ ,R divides sidesB C ,A C , and A B , respec...

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  20. If the angles of a triangle are 30^0a n d45^0 and the included side is...

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