Home
Class 11
MATHS
In triangle ABC, line joining the cir...

In triangle ABC, line joining the circumcenter and orthocentre is parallel to side AC, then the value of `t a n AtanCi se q u a lto` `sqrt(3)` (b) 3 (c) `3sqrt(3)` (d) none of these

Text Solution

Verified by Experts

`CE=RcosB`
`OF=2RcosAcosC`
`RcosB=2RcosAcosC`
`-cos(A+B)=2cosAcosC`
`-(cosAcosC-sinAsinC)=2cosAcosC`
`sinAsinC=3cosAcosC`
`tanAtanC=3`.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|482 Videos

Similar Questions

Explore conceptually related problems

In triangle ABC, line joining the circumcenter and orthocenter is parallel to side AC, then the value of tan A tan C is equal to

In triangle ABC, the line joining the circumcenter and incenter is parallel to side AC, then cos A + cos C is equal to

In triangle ABC ,the line joining the circumcenter and incenter is parallel to side AC, then cos A+cos C is equal to -1 (b) 1 (c) -2(d)2

In a triangle the lengths of the two larger sides are 10 and 9, respectively.If the angles are in AP,then the length of the third side can be (a) sqrt(91) (b) 3sqrt(3) (c) 5 (d) none of these

Let the line joining through orthocentre and circumcentre of the triangle ABC is parallel to the base BC .If tan B=k cot C then the value of k is equal to

In a triangle, the lengths of the two larger sides are 10 and 9, respectively. If the angles are in A.P., then the length of the third side can be (a) 5-sqrt(6) (b) 3sqrt(3) (c) 5 (d) 5+sqrt(6)

If the sides of a right-angled triangle are in A.P., then the sines of the acute angles are 3/5,4/5 b. 1/(sqrt(3)),sqrt(2/3) c. 1/2,(sqrt(3))/2 d. none of these

Given b=2,c=sqrt(3),/_A=30^(0), then inradius of o+ABC is (sqrt(3)-1)/(2) (b) (sqrt(3)+1)/(2) (c) (sqrt(3)-1)/(4) (d) none of these

If in a triangle ABC,3sin A=6sin B=2sqrt(3)sin C then the value of /_A=

If A(1,p^(2)),B(0,1) and C(p,0) are the coordinates of three points,then the value of p for which the area of triangle ABC is the minimum is (1)/(sqrt(3))( b) -(1)/(sqrt(3))(1)/(sqrt(2)) (d) none of these

CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Which of the following is not the quadratic equation whose roots are c...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Solve 2tantheta-cottheta=-1

    Text Solution

    |

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

    Text Solution

    |

  10. If cos(A+B+C)=cosAcosBcosC , then find the value of (8sin(B+C)sin(C+A)...

    Text Solution

    |

  11. In the given figure, what is the radius of the inscribed circle? 3/2 ...

    Text Solution

    |

  12. Solve tan3theta=-1

    Text Solution

    |

  13. If sinA=sin^2Ba n d2cos^2A=3cos^2B then the triangle A B C is right...

    Text Solution

    |

  14. In triangle A B C , if cotA *cotC=1/2a n dcot B* cotC=1/(18), then t...

    Text Solution

    |

  15. If in a triangle A B C ,(1+cosA)/a+(1+cosB)/b+(1(cosC))/c =(k^2(1+cos...

    Text Solution

    |

  16. Solve tantheta+tan2theta+sqrt(3)tanthetatan2theta=sqrt(3)

    Text Solution

    |

  17. The product of the sines of the angles of a triangle is p and the prod...

    Text Solution

    |

  18. If (sinx)/a=(cosx)/b=(tanx)/c=k , then b c+1/(c k)+(a k)/(1+b k) is eq...

    Text Solution

    |

  19. In A B C ,a=5,b=12 ,c=90^0a n dD is a point on A B so that /B C D=45^...

    Text Solution

    |

  20. Solve tan5theta=cot2theta

    Text Solution

    |