Home
Class 11
MATHS
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

Text Solution

Verified by Experts

`(a^2+b^2+c^2)/R^2=((2RsinA)^2+(2RsinB)^2+(2Rsinc)^2)/R^2`
`4(sin^2A+sin^2B+sin^2C)`
`4*2(1+cosAcosBcosC)`
`8(1+cosAcosBcosC)`
`8(1+1/8)`
`8(9/8)`
`9`
Option C is correct.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|381 Videos

Similar Questions

Explore conceptually related problems

The minimum value of 2^(x^2-3)^(3+27) is a) 2^(27) (b) 2 (c) 1 (d) none of these

If in triangle A B C ,Delta =a^2-(b-c)^2 , then find the value of tan(A/2).

In triangle ABC, prove that the maximum value of tan(A/2)tan(B/2)tan(C/2)i s R/(2s)

In triangle A B C ,b^2 sin2C+c^2sin2B=2bc where b=20 ,c=21 , then inradius= (a)4 (b) 6 (c) 8 (d) 9

In A B C with fixed length of B C , the internal bisector of angle C meets the side A Ba tD and the circumcircle at E . The maximum value of C D.D E is c^2 (b) (c^2)/2 (c) (c^2)/4 (d) none of these

In any triangle ABC ,c^2 sin 2 B + b^2 sin 2 C is equal to

If circumradius of triangle is 2, then the maximum value of (abc)/(a+b+c) is

In any triangle, the minimum value of r_1r_2r_3//r^3 is equal to 1 (b) 9 (c) 27 (d) none of these

In a A B C ,/_B=90^0 and b+a=4. The area of the triangle is maximum when /_C is (a) pi/4 (b) pi/6 (c) pi/3 (d) none of these

In triangle A B C , if r_1=2r_2=3r_2, then a : b is equal to 5/4 (b) 4/5 (c) 7/4 (d) 4/7

CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. In A B C ,A=(2pi)/3,b-c=3sqrt(3)c m and area of A B C=(9sqrt(3))/2c ...

    Text Solution

    |

  2. The general value of theta satisfying the equation tan^2theta+sec2thet...

    Text Solution

    |

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

    Text Solution

    |

  4. Solve sqrt(5-2 sin x)=6 sin x-1

    Text Solution

    |

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

    Text Solution

    |

  6. Solve sin^3thetacostheta-cos^3thetasintheta=1/4dot

    Text Solution

    |

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

    Text Solution

    |

  8. Solve 4costheta-3sectheta=tantheta

    Text Solution

    |

  9. P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) ...

    Text Solution

    |

  10. Solve the equation 2cos^2theta+3sintheta=0

    Text Solution

    |

  11. In A B C , if b^2+c^2=2a^2, then value of (cotA)/(cotB+cotC) is 1/2 ...

    Text Solution

    |

  12. Find the number of solution of [cosx]+|sinx|=1, x inpilt=xlt=3pi (whe...

    Text Solution

    |

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

    Text Solution

    |

  14. If the equation asinx+cos2x=2a-7 possesses a solution, then find the ...

    Text Solution

    |

  15. In A B C ,(a+b+c)(b+c-a)=k b c if k<0 (b) k >0 =<k<4 (d) k >4

    Text Solution

    |

  16. Find the number of solution of the equation e^(sinx)-e^(-sinx)-4=0

    Text Solution

    |

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

    Text Solution

    |

  18. If x in (0,2pi)a n dy in (0,2pi) , then find the number of distinct or...

    Text Solution

    |

  19. In a triangle A B CifB C=1a n dA C=2, then what is the maximum possibl...

    Text Solution

    |

  20. Find the number of roots of the equation 16sec^3theta-12tan^2theta-4se...

    Text Solution

    |