Home
Class 12
MATHS
In the triangle ABC, lines OA,OB and OC ...

In the triangle ABC, lines `OA,OB` and `OC` are drawn so that angles OAB, OBC and OCA are each equal to `omega`, prove that `cotomega=cotA+cotB+cotC`

Text Solution

Verified by Experts

The correct Answer is:
`cot w =cot A +cot B +cot C.`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise SOLVED EXAMPLES|1 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise For Sesssion 1|20 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|52 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

Similar Questions

Explore conceptually related problems

Angles A, B and C of a triangle ABC are equal to each other. Prove that DeltaABC is equilateral.

If A,B,C are the angles of a triangle and sin^3 theta= sin (A- theta)sin (B-theta)sin (C-theta) , prove that: cot theta= cotA+cotB +cotC .

Bisectors of angles B and C of an isoscels triangles ABC with AB=AC intersects each other at O. prove that external angle adjacent to angleABC is equal to angleBOC .

In a triangle ABC , if b^2 + c^2 = 3a^2 , then cotB + cotC-cotA is equal to

Prove that the triangle ABC is equilateral if cotA+cotB+cotC=sqrt3

In the triangle OAB , M is the midpoint of AB, C is a point on OM, such that 2 OC = CM . X is a point on the side OB such that OX = 2XB. The line XC is produced to meet OA in Y. Then (OY)/(YA)=

If O and H be the circumcentre and orthocentre respectively of triangle ABC, prove that vec OA+ vec OB+ vec OC= vec OH .

ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. In the triangle ABC, lines OA,OB and OC are drawn so that angles OAB, ...

    Text Solution

    |

  2. Prove that 2sin^2(pi/6) - sec^2(pi/3)= -7/2

    Text Solution

    |

  3. In a triangle the sum of two sides is x and the product of the same is...

    Text Solution

    |

  4. Consider a triangle A B C and let a , b and c denote the lengths of th...

    Text Solution

    |

  5. Solution of differential equation 2xy dy / dx = x^2 + 3y^2 is .

    Text Solution

    |

  6. Let PQR be a triangle of area Delta with a = 2, b = 7//2, and c = 5//2...

    Text Solution

    |

  7. If the angle A ,Ba n dC of a triangle are in an arithmetic propression...

    Text Solution

    |

  8. Let A B C be a triangle such that /A C B=pi/6 and let a , b and c deno...

    Text Solution

    |

  9. A triangle A B C with fixed base B C , the vertex A moves such that co...

    Text Solution

    |

  10. Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...

    Text Solution

    |

  11. A straight line through the vertex P of a triangle P Q R intersects th...

    Text Solution

    |

  12. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  13. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  14. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  15. Internal bisector of /A of triangle ABC meets side BC at D. A line dra...

    Text Solution

    |

  16. One angle of an isosceles triangle is 120^0 and the radius of its incr...

    Text Solution

    |

  17. In Delta ABC, which one is true among the following ?

    Text Solution

    |

  18. Let a vertical tower A B have its end A on the level ground. Let C be ...

    Text Solution

    |

  19. ABCD is a trapezium such that AB and CD are parallel and BC bot CD. If...

    Text Solution

    |

  20. For a regular polygon, let r and R be the radii of the inscribed and t...

    Text Solution

    |

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

    Text Solution

    |