Home
Class 11
MATHS
The exradii r1,r2 and r3 of /\A B C ...

The exradii `r_1,r_2` and `r_3` of ` /_\A B C` are in H.P. Show that its sides `a , ba n dc` are in `AdotPdot`

Text Solution

Verified by Experts

`r_1=D/(s-a),r_2=D/(s-b),r_3=D/(s-c)`
`D/(s-a),D/(s-b),D/(s-c)` are in HP
s-a,s-b,s-c are in Ap
a,b,c are in AP.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|482 Videos

Similar Questions

Explore conceptually related problems

The exradii r_(1), r_(2), and r_(3) " of " Delta ABC are in H.P. show that its sides a, b, and c are in A.P.

The exradii r_(1), r_(2), r_(3)" of "DeltaABC and in HP, show that it’s the arithmetic mean of a and c.

If r_(1), r_(2), r_(3) in triangle be in H.P., then the sides are :

If a,b,c are in AP, then show that r_(1), r_(2), r_(3) are in HP.

The radii r_(1), r_(2), r_(3) of the escribed circles of the triangle ABC are in H.P. If the area of the triangle is 24 cm^(2) and its perimeter is 24 cm, then the length of its largest side is

CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Let alpha,beta,gamma>0a n dalpha+beta+gamma=pi/2dot Then prove that sq...

    Text Solution

    |

  2. The number of solution of sin^4x-cos^2xsinx+2sin^2x+sinx=0in0lt=xlt=3p...

    Text Solution

    |

  3. The exradii r1,r2 and r3 of /\A B C are in H.P. Show that its side...

    Text Solution

    |

  4. Solve 7cos^2theta+3sin^2theta=4

    Text Solution

    |

  5. If sintheta+costheta=1/5"and"0 le theta ltpi, thentantheta is

    Text Solution

    |

  6. In A B C Prove that cos^2A/2+cos^2B/2+cos^2C/2lt=9/4dot In cos^2A/2...

    Text Solution

    |

  7. The exradii r1,r2 and r3 of /\A B C are in H.P. Show that its side...

    Text Solution

    |

  8. Find the number of roots of the equation tan(x+pi/6)=2tanx ,forx in (0...

    Text Solution

    |

  9. In A B C , prove that cos e c A/2+cos e c B/2+cos e c C/2geq6.

    Text Solution

    |

  10. If x=(2sintheta)/(1+costheta+sintheta),t h e n(1-costheta+sintheta)/(1...

    Text Solution

    |

  11. Solve the equation 2(cos x+cos2x)+sin2x(1+2cos x)=2sinx for (-pilt=xlt...

    Text Solution

    |

  12. Which of the following is not the quadratic equation whose roots are c...

    Text Solution

    |

  13. If A+B+C=pi, prove that (tanA)/(tanBdottanC)+(tanB)/(tanAdott a n C...

    Text Solution

    |

  14. In triangle ABC, line joining the circumcenter and orthocentre is p...

    Text Solution

    |

  15. Solve 8sinx=(sqrt(3))/(cosx)+1/(sinx)

    Text Solution

    |

  16. If cos e ctheta-cottheta=q , then the value of cos e ctheta is (a)q...

    Text Solution

    |

  17. If A+B+C=pi , prove that cotA+cotB+cotC-cos e cAdotcos e cBdotcos e cC...

    Text Solution

    |

  18. Let D be the middle point of the side B C of a triangle A B Cdot If th...

    Text Solution

    |

  19. Solve 2tantheta-cottheta=-1

    Text Solution

    |

  20. If sec^4theta+sec^2theta=10+tan^4theta+tan^2theta, then sin^2theta= 2...

    Text Solution

    |