Home
Class 12
MATHS
The centres of two circles C(1) and C(2...

The centres of two circles `C_(1) and C_(2)` each of unit radius are at a distance of 6 unit from each other. Let P be the mid-point of the line segment joining the centres of `C_(1) and C_(2)` and C be a circle touching circles `C_(1) and C_(2)` externally. If a common tangent to `C_(1)` and C passing through P is also a common tangent to `C_(2)` and C, then the radius of the circle C, is

Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|8 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

The centres of two circles C1 and C2 each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1 and C2 and C be a circle touching circles C1 and C2 externally. If a common tangent to C1 and C passing through P is also a common tangent to C2 and C, then the radius of the circle C is

Circles C_(1) and C_(2) of radii r and R respectively, touch each other as shown in the figure. The lime l, which is parallel to the line joining the centres of C_(2) and C_(2) is tangent to C_(1) at P and intersects C_(2) at A,B.If R^(2)=2r^(2) , then angleAOB equals-

Let C_(1) and C_(2) be externally tangent circles with radius 2 and 3 respectively.Let C_(1) and C_(2) both touch circle C_(3) internally at point A and B respectively.The tangents to C_(3) at A and B meet at T and TA=4, then radius of circle C_(3) is:

C_(1) and C_(2) are circle of unit radius with centers at (0,0) and (1,0), respectively,C_(3) is a circle of unit radius.It passes through the centers of the circles C_(1) and C_(2) and has its center above the x-axis.Find the equation of the common tangent to C_(1)andC_(3) which does not pass through C_(2).

If a circle C passing through (4,0) touches the circle x^(2)+y^(2)+4x-6y-12=0 externally at a point (1,-1), then the radius of the circle C is :

The internal common tangents to two circles with centre C_(1) and C_(2) intersect the line joining C_(1) and C_(2) at P and the two direct common tangents intersects the line joining C_(1) and C_(2) at Q. The length C_(1)P,C_(1)C_(2) are C_(1) Q are in

AB is the common tangent to the circles C_(1) and C_(2).C_(1) and C_(2) are touching externally at C.AD and DC are two chords of the circle C_(1) and BE and CE are two chords of the circle C_(2) Find the measure of /_ADC+/_BEC

The line L_(1)-=3x-4y+1=0 touches the circles C_(1) and C_(2) . Centers of C_(1) and C_(2) are A_(1)(1, 2) and A_(2)(3, 1) respectively Then, the length (in units) of the transverse common tangent of C_(1) and C_(2) is equal to

ARIHANT MATHS-CIRCLE -Exercise (Subjective Type Questions)
  1. Consider a curve ax^2 + 2hxy + by^2-1=0 and a point P not on the curve...

    Text Solution

    |

  2. Tangents drawn from the point P(1,8) to the circle x^2 +y^2 -6x -4y-11...

    Text Solution

    |

  3. The centres of two circles C(1) and C(2) each of unit radius are at a...

    Text Solution

    |

  4. If P and Q are the points of intersection of the circles x^2+""y^2+...

    Text Solution

    |

  5. If the circle x^2+y^2-4x-8y-5=0 intersects the line 3x-4y=m at two dis...

    Text Solution

    |

  6. The circle passing through the point (-1,0) and touching the y-axis at...

    Text Solution

    |

  7. The straight line 2x-3y = 1 divides the circular region x^2+ y^2 le6 i...

    Text Solution

    |

  8. The two circles x^2+""y^2=""a x and x^2+""y^2=""c^2(c"">""0) touch eac...

    Text Solution

    |

  9. The locus of the middle point of the chord of contact of tangents draw...

    Text Solution

    |

  10. A tangent PT is drawn to the circle x^2 + y^2= 4 at the point P(sqrt3,...

    Text Solution

    |

  11. A tangent PT is drawn to the circle x^2 + y^2= 4 at the point P(sqrt3,...

    Text Solution

    |

  12. The length of the diameter of the circle which touches the x-axis at ...

    Text Solution

    |

  13. The circle passing through (1, -2) and touching the axis of x at (3...

    Text Solution

    |

  14. Circle(s) touching x-axis at a distance 3 from the origin and having a...

    Text Solution

    |

  15. Let C be the circle with centre at (1, 1) and radius = 1. If T is t...

    Text Solution

    |

  16. A circle S passes through the point (0, 1) and is orthogonal to the ci...

    Text Solution

    |

  17. Locus of the image of the point (2, 3) in the line (2x-3y""+""4)""+...

    Text Solution

    |

  18. The number of common tangents to the circles x^(2)+y^(2)-4x-6y-12=0 a...

    Text Solution

    |

  19. The centres of those circles which touch the circle, x^2+y^2-8x-8y-4=0...

    Text Solution

    |

  20. If one of the diameters of the circle, given by the equation, x^2+y^2-...

    Text Solution

    |