Home
Class 12
MATHS
perpendiculars are drawn from the angles...

perpendiculars are drawn from the angles `A , Ba n dC` of an acute-angled triangle on the opposite sides, and produced to meet the circumscribing circle. If these produced parts are `alpha,beta,gamma` , respectively, then show that `a/alpha+b/beta+c/gamma=2(tanA+tanB+t a nC)dot`

Text Solution

Verified by Experts

The correct Answer is:
`(a)/(alpha) +(b)/(beta)+ (c)/(gamma) =2 (tan A+ tan B+ tan C)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise SOLVED EXAMPLES|1 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise Exercise For Sesssion 1|20 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|51 Videos

  • SEQUENCES AND SERIES

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

Similar Questions

Explore conceptually related problems

Perpendiculars are drawn from the angles A, B and C of an acute-angled triangle onthe opposite sides, and produced to meet the circumscribing circle. If these produced parts are alpha., beta, gamma, respectively, then show that, then show that a/alpha+b/beta+c/gamma=2(tanA+tanB+tanC).

If the direction angles of a line are alpha, beta and gamma respectively, then cos 2 alpha + cos 2 beta + cos 2gamma is equal to

If a line makes angles alpha,beta,gamma with the axes respectively tehn cos2alpha+cos2beta+cos2gamma= -2 b. -1 c. 1 d. 2

PQ and QR are two focal chords of an ellipse and the eccentric angles of P,Q,R are 2alpha, 2beta, 2 gamma , respectively then tan beta gamma is equal to

If a vector makes angle alpha,beta,gamma with OX, OY and OZ respectively, then write the value of sin^2alpha+sin^2beta+sin^2gammadot

If a vector makes angles alpha,beta,gamma. with . OX ,O Ya n dO Z respectively, prove that sin^2alpha+sin^2beta+sin^2gamma=2.

If a line makes angles alpha, beta, gamma with the axes then cos2alpha +cos2beta+cos2gamma = (A) -2 (B) -1 (C) 1 (D) 2

If vec(A) makes an angle alpha, beta and gamma from x,y and z axis respectively then sin^(2)alpha+sin^(2) beta+sin^(2) gamma=

If the distances of the vertices of a triangle =ABC from the points of contacts of the incercle with sides are alpha,betaa n dgamma then prove that r^2=(alphabetagamma)/(alpha+beta+gamma)

Area of the triangle formed by the tangents at the point on the ellipse x^2/a^2+y^2/b^2=1 whose eccentric angles are alpha,beta,gamma is

ARIHANT MATHS ENGLISH-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. perpendiculars are drawn from the angles A , Ba n dC of an acute-angle...

    Text Solution

    |

  2. In a triangle XYZ, let x, y, z be the lengths of sides opposite to the...

    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 , ba n dc denote the lengths of th...

    Text Solution

    |

  5. about to only mathematics

    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

    |