Home
Class 10
MATHS
Two parallel tangents of a circle meet a...

Two parallel tangents of a circle meet a third tangent at points P and Q. Prove that PQ subtends a right angle at the centre.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TANGENTS AND INTERSECTING CHORDS

    ICSE|Exercise EXERCISE 18 (B)|18 Videos

  • TANGENTS AND INTERSECTING CHORDS

    ICSE|Exercise EXERCISE 18 (C)|42 Videos

  • TANGENTS AND INTERSECTING CHORDS

    ICSE|Exercise EXERCISE 18 (C)|42 Videos

  • SPECIMEN QUESTION PAPER (MATHEMATICS)

    ICSE|Exercise Section C|12 Videos

  • TRIGONOMETRICAL IDENTITIES

    ICSE|Exercise QUESTIONS|22 Videos

Similar Questions

Explore conceptually related problems

Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

In Fig. 10.62, P O_|_Q O . The tangents to the circle at P and Q intersect at a point T . Prove that P Q and O T are right bisectors of each other. (FIGURE)

X Y and Xprime Yprime are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting X Y at A and XprimeYprime at B. Prove that /_A O B\ =\ 90^0

Prove that the portion of the tangent to an ellipse intercepted between the ellipse and the directrix subtends a right angle at the corresponding focus.

l and m are two parallel tangents to a circle with centre O, touching the circle at A and B respectively. Another tangent at C intersects the line l at D and m at E. Prove that /_DOE=90^@.

If the chord of contact of the tangents drawn from the point (h , k) to the circle x^2+y^2=a^2 subtends a right angle at the center, then prove that h^2+k^2=2a^2dot

In the figure, PO_|_QO. The tangents to the circle with centre O at P and Q intersect at a point T. Prove that PQ and OT are right bisectors of each other.

Two circles with centres A and B intersect each other at points P and Q. Prove that the centre-line AB bisects the common chord PQ perpendicularly.

If z_(0),z_(1) represent points P and Q on the circle |z-1|=1 taken in anticlockwise sense such that the line segment PQ subtends a right angle at the center of the circle, then z_(1)=

If bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle, circumscribing it at the points P and Q, prove that PQ is a diameter of the circle.

ICSE-TANGENTS AND INTERSECTING CHORDS-EXERCISE 18(A)
  1. Two concentric circles are of radii 5 cm and 3 cm. Find the length ...

    Text Solution

    |

  2. Three circles touch each other externally. A triangle is formed when t...

    Text Solution

    |

  3. A quadrilateral ABCD is ABCD is drawn to circumscribe a circle. Prove ...

    Text Solution

    |

  4. If the sides of a parallelogram touch a circle prove that the parallel...

    Text Solution

    |

  5. From the given figure, prove that : AP+BQ+CR=BP+CQ+AR Also show tha...

    Text Solution

    |

  6. In the figure if AB=AC then prove that BR=CR

    Text Solution

    |

  7. Radii of two circles are 6.3 cm and 3.6 cm. State the distance between...

    Text Solution

    |

  8. From a point P outside a circle, with centre O, tangents PA and PB are...

    Text Solution

    |

  9. In the given figure, two circles touch each other externally at point ...

    Text Solution

    |

  10. Tangents AP and AQ are drawn to a circle, with centre O, from an exter...

    Text Solution

    |

  11. Two parallel tangents of a circle meet a third tangent at points P and...

    Text Solution

    |

  12. ABC is a right angled triangle with AB=12 cm and AC=13 cm. A circle, w...

    Text Solution

    |

  13. In a triangle ABC, the incircle (centre O) touches BC , CA and AB at p...

    Text Solution

    |

  14. In the following figure PQ and PR are tangents to the circle with the ...

    Text Solution

    |

  15. In the giben figure, AB is the diameter of the circle, with centre O a...

    Text Solution

    |

  16. In quadrilateral ABCD angled D=90^(@), BC=38cm and DC=25cm. A circle i...

    Text Solution

    |

  17. In the given figure, PT touches the circle with centre O at point R. D...

    Text Solution

    |

  18. PT is a tangent to the circle at T. If /ABC=70^(@) and /ACB=50^(@), ...

    Text Solution

    |

  19. In the given figure, O is the centre of the circumcircle of triangleAB...

    Text Solution

    |

  20. In the given PQ is a tangent to the circle at A. AB and AD are bisecto...

    Text Solution

    |