Home
Class 10
MATHS
If angle between two tangents drawn from...

If angle between two tangents drawn from a point P to a circle of radius a and centre 0 is `60^(@)` then `OP=asqrt3`.

Text Solution

AI Generated Solution

To solve the problem, we need to find the length of OP given that the angle between the two tangents drawn from point P to the circle is \(60^\circ\) and the radius of the circle is \(a\). ### Step-by-step Solution: 1. **Understanding the Geometry**: - Let \(O\) be the center of the circle and \(A\) and \(B\) be the points where the tangents from point \(P\) touch the circle. - The angle \(APB\) is given as \(60^\circ\). ...
Promotional Banner

Topper's Solved these Questions

  • ARITHMETIC PROGRESSIONS

    NCERT EXEMPLAR|Exercise Arithmetic Progressions|71 Videos
  • CONSTRUCTIONS

    NCERT EXEMPLAR|Exercise Exercise 10.4 Long Answer type Questions|7 Videos

Similar Questions

Explore conceptually related problems

Write true or false and state reason If angle between two tangents drawn from a point P to a circle of radius a and centre 0 is 90^(@) then OP=asqrt2 .

If angle between two tangents drawn from a point P to a circle of radius 'a' and the centre O is 90^(@) then prove that OP=sqrt(a)

If the angle between two tangents drawn from an external point P to a circle of radius 'a' and center O , is 60^(@), then find the length of OP.

The angle between tangents drawn from a point P to the circle x^2+y^2+4x-2y-4=0 is 60^@ Then locus of P is

What is the angle between the two tangents drawn from an external point to a circle and the angle subtended by the line-segment joining the points of the contact at the centre.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact at the centre.

Prove that the angle between two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact at the centre.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

The length of tangent from an external point P on a circle with centre 0 is always less than OP.

NCERT EXEMPLAR-CIRCLES-Circles
  1. The angle between two tangents to a circle may be 0^(@).

    Text Solution

    |

  2. Write true or false and state reason If angle between two tangents dra...

    Text Solution

    |

  3. If angle between two tangents drawn from a point P to a circle of radi...

    Text Solution

    |

  4. The tangent to the circumcircle of an isosceles DeltaABC at A, in whic...

    Text Solution

    |

  5. If a number of circles pass through the end points P and Q of a line s...

    Text Solution

    |

  6. If a number of circles pass through the end points P and Q of a line s...

    Text Solution

    |

  7. AB is a diameter of a circle and AC is its chord such that angleBAC=30...

    Text Solution

    |

  8. Out of the 2 concentric circle the radius of the outer circle is 5 cm ...

    Text Solution

    |

  9. Two tangents PQ and PR are drawn from an external point to a circle wi...

    Text Solution

    |

  10. Prove that the centre of a circle touching two intersecting lines lies...

    Text Solution

    |

  11. If from an external point B of a circle with centre O, two tangents BC...

    Text Solution

    |

  12. In figure, AB and CD are common tangents to two circles of unequal rad...

    Text Solution

    |

  13. In figure, AB and CD are common tangents to two circles of equal radii...

    Text Solution

    |

  14. In figure, common tangents AB and CD to two circles intersect at E. P...

    Text Solution

    |

  15. A chord PQ of a circle is parallel to the tangent drawn at a point R ...

    Text Solution

    |

  16. Prove that the tangents drawn at the end points of a chord of a circle...

    Text Solution

    |

  17. Prove that a diameter AB of a circle bisects all those chords which ar...

    Text Solution

    |

  18. If a hexagon ABCDEF circumscribe a circle, prove that AB + CD + EF=BC+...

    Text Solution

    |

  19. Let's denotes the semi-perimeter of a DeltaABC in which BC=a, CA=b and...

    Text Solution

    |

  20. From an external point P, two tangents, PA and PB are drawn to a circl...

    Text Solution

    |