Home
Class 10
MATHS
Two circles touch each other internally ...

Two circles touch each other internally at point P. QPR is the tangent at P, segments PAB and PCD meet circles at points, A,B,C and D as shown in the figure.
Show that chord AC is parallel to chord BD.

Text Solution

Verified by Experts

The correct Answer is:
AC is parallel to BD.
Promotional Banner

Topper's Solved these Questions

  • TANGENTS AND INTERSECTING CHORDS

    ICSE|Exercise EXERCISE 18(A)|24 Videos

  • TANGENTS AND INTERSECTING CHORDS

    ICSE|Exercise EXERCISE 18 (B)|18 Videos

  • SPECIMEN QUESTION PAPER (MATHEMATICS)

    ICSE|Exercise Section C|12 Videos

  • TRIGONOMETRICAL IDENTITIES

    ICSE|Exercise QUESTIONS|22 Videos

Similar Questions

Explore conceptually related problems

Two circles intersect each other at point A and B. Their common tangent touches the circles at points P and Q as shown in the figure. Show that the angles PAQ and PBQ are supplementary.

Two circles touch each other externally at point P. Q is a point on the common tangent through P. Prove that the tangents QA and QB are equal.

Two circles touch each other extermally at point P. APC and BPD are straight lines. Show that : Delta PAB and Delta PCD are similar

Two circles touch each other extermally at point P. APC and BPD are straight lines. Show that : AP is parallel to CD.

Two circles touch each other internally. Show that the tangents drawn to the two circles from any point on the common tangent, are equal in length.

In Figure, two circles touch each other at the point C . Prove that the common tangent to the circles at C , bisects the common tangent at P and Q .

In the figure, two circles touch each other at the point C.Prove that the common tangents to the circles at C, bisect the common tangents at P and Q.

In the given figure, two circles touch each other externally at point P. AB is the direct common tangent of these circles. Prove that: (i) tangent at point P bisects AB (ii) angle APB=90^(@)

Two circles intersect each other at points A and B. A straight line PAQ cuts the circles at P and Q. If the tangents at P and Q intersect at point T, show that the points P, B, Q and T are concylic.

ICSE-TANGENTS AND INTERSECTING CHORDS-EXERCISE 18 (C)
  1. Two circles touch each other internally at point P. QPR is the tangent...

    Text Solution

    |

  2. Prove that , Of any two chords of a circle, show that the one which is...

    Text Solution

    |

  3. OABC is a rhombus whose three vertices. A, B and C lie on a circle wit...

    Text Solution

    |

  4. Two circles with centres A and B and radii 5 cm and 3 cm, touch each o...

    Text Solution

    |

  5. Two chords A B and A C of a circle are equal. Prove that the centre of...

    Text Solution

    |

  6. The diameter and a chord of a circle have a common end point. If the l...

    Text Solution

    |

  7. ABCD is a cyclic quadrilateral in which BC is paralleld to AD, angle A...

    Text Solution

    |

  8. In the given figure, C and D are points on the semi circle described o...

    Text Solution

    |

  9. In cyclic quadrilateral ABCD,/A=3/C and /D=5 /B. Find the measure of e...

    Text Solution

    |

  10. Prove that the circle drawn on any one of the equal sides of an iso...

    Text Solution

    |

  11. Bisectors of vertex angles A, B and C of a triangle ABC intersect its ...

    Text Solution

    |

  12. In the figure AB is the chord of a circle with centre O and DOC is a l...

    Text Solution

    |

  13. Prove that the perimeter of a right triangle is equal to the sum of th...

    Text Solution

    |

  14. . Prove that the tangent drawn at the mid-point of an arc of a circle ...

    Text Solution

    |

  15. In the given figure, MN is the common chord of two intersecting circle...

    Text Solution

    |

  16. In the given figure, ABCD is a cyclicquadrilateral, PQ is tangent to t...

    Text Solution

    |

  17. The given figure shows a circle with centre O and BCD is tangent to it...

    Text Solution

    |

  18. ABC is a right triagle with angle B=90^(@) . A circle with BC as diame...

    Text Solution

    |

  19. In the given figure AC=AE Show that (i) CP=EP (ii) BP=DP

    Text Solution

    |

  20. ABCDE is a cyclic pentagon with centre of its circumcircle alt point O...

    Text Solution

    |

  21. In the given figure O is the centre of the circle. Tangents at A and B...

    Text Solution

    |