Home
Class 12
MATHS
Tangent are parallel to the three sides ...

Tangent are parallel to the three sides are drawn to the in-circle. If x,y,z are the lengths of parts of the tangents with in triangle, then prove that `x/a+y/b+z/c=1.`

Text Solution

Verified by Experts

The correct Answer is:
`((x)/(a)+(y)/(b)+(z)/(c ))=1`
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

If tan^-1x + tan^-1y + tan^-1z = pi , then prove that: x + y + z = xyz.

If the length of the tangent drawn from (f, g) to the circle x^2+y^2= 6 be twice the length of the tangent drawn from the same point to the circle x^2 + y^2 + 3 (x + y) = 0 then show that g^2 +f^2 + 4g + 4f+ 2 = 0 .

If tan^-1 x + tan^-1y - tan^-1z = 0 , then prove that x + y + xyz = z.

The equation of one of the tangents to x^2/3-y^2/2=1 which is parallel to y = x is :

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Tangents drawn from a point on the circle x^2+y^2=9 to the hyperbola x^2/25-y^2/16=1, then tangents are at angle

The equation of the tangent parallel to y=x drawn to x^2/3-y^2/2 =1 is :

If the pair of tangents are drawn from the point (4,5) to the circle x^(2)+y^(2)-4x-2y-11=0 , then (i) Find the length of chord of contact. (ii) Find the area of the triangle fromed by a pair of tangents and their chord of contact. (iii) Find the angle between the pair of tangents.

The tangent of the curve y = 2x^2 - x + 1 is parallel to the line y = 3x + 9 at the point

ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Tangent are parallel to the three sides are drawn to the in-circle. If...

    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

    |