Home
Class 12
MATHS
If the chord of contact of the tangents ...

If the chord of contact of the tangents drawn from a point on the circle `x^2+y^2+y^2=a^2` to the circle `x^2+y^2=b^2` touches the circle `x^2+y^2=c^2` , then prove that `a ,b` and `c` are in GP.

Text Solution

Verified by Experts

The correct Answer is:
`=>` a, b, c are in GP.
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise For Session 1|18 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise For Session 2|17 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|43 Videos

Similar Questions

Explore conceptually related problems

chord of contact of the tangents drawn from a point on the circle x^(2)+y^(2)=81 to the circle x^(2)+y^(2)=b^(2) touches the circle x^(2)+y^(2)=16 , then the value of b is

If the chord of contact of the tangents from a point on the circle x^2 + y^2 = a^2 to the circle x^2 + y^2 = b^2 touch the circle x^2 +y^2 = c^2 , then the roots of the equation ax^2 + 2bx + c = 0 are necessarily. (A) imaginary (B) real and equal (C) real and unequal (D) rational

The chord of the contact of tangents drawn from a point on the circle x^(2) + y^(2) = a^(2) to the circle x^(2) = y^(2) = b^(2) touches the circle x^(2) + y^(2) =c^(2) such that b^(m)= a^(n)c^(p) , where m,n p in N and m,n,p are prime to each other , then the value of m+ n+ p -3 is :

The length of the chord of contact of the tangents drawn from the point (-2,3) to the circle x^2+y^2-4x-6y+12=0 is:

If the chord of contact of tangents from a point P(h, k) to the circle x^(2)+y^(2)=a^(2) touches the circle x^(2)+(y-a)^(2)=a^(2) , then locus of P is

The angle between the tangents drawn from a point on the director circle x^(2)+y^(2)=50 to the circle x^(2)+y^(2)=25 , is

If two tangents are drawn from a point to the circle x^(2) + y^(2) =32 to the circle x^(2) + y^(2) = 16 , then the angle between the tangents is

If the chord of contact of tangents from a point (x_(1),y_(1)) to the circle x^(2)+y^(2)=a^(2) touches the circle (x-a)^(2)+y^(2)=a^(2), then the locus of (x_(1),y_(1)) is

ARIHANT MATHS-CIRCLE -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If the chord of contact of the tangents drawn from a point on the c...

    Text Solution

    |

  2. A circle is given by x^2 + (y-1) ^2 = 1, another circle C touches it e...

    Text Solution

    |

  3. If the circles x^2+y^2+2a x+c y+a=0 and points Pa n dQ , then find the...

    Text Solution

    |

  4. A circle touches the x-axis and also touches the circle with center (...

    Text Solution

    |

  5. If a circle passes through the point (a, b) and cuts the circlex x^2+y...

    Text Solution

    |

  6. Let ABCD be a square of side length 2 units. C2 is the circle through ...

    Text Solution

    |

  7. ABCD is a square of side length 2 units. C(1) is the circle touching ...

    Text Solution

    |

  8. ABCD is a square of side length 2 units. C(1) is the circle touching ...

    Text Solution

    |

  9. If the lines 3x-4y-7 = 0 and 2x-3y-5=0 are two diameters of a circle o...

    Text Solution

    |

  10. Let C be the circle with centre (0, 0) and radius 3 units. The equatio...

    Text Solution

    |

  11. Tangents are drawn from the point (17, 7) to the circle x^2+y^2=169, S...

    Text Solution

    |

  12. Consider a family of circles which are passing through the point (-...

    Text Solution

    |

  13. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

    Text Solution

    |

  14. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

    Text Solution

    |

  15. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

    Text Solution

    |

  16. Consider: L1:2x+3y+p-3=0 L2:2x+3y+p+3=0 where p is a real number and...

    Text Solution

    |

  17. The point diametrically opposite to the point P(1, 0) on the circle x^...

    Text Solution

    |