Home
Class 9
MATHS
If a diameter of a circle bisects eac...

If a diameter of a circle bisects each of the two chords of a circle, prove that the chords are parallel.

Text Solution

Verified by Experts

The correct Answer is:
`4 sqrt(6) cm`
Let AB and CD be two chords of a circle with centre O. Suppose a diameter POQ bisects the at L and M . The,
`OL _|_ AB` and `OM _|_ CD`.
Thus,`/_ ALM = /_ LMD implies AB ||CD`.
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    RS AGGARWAL|Exercise EXERCISE 12B|18 Videos

  • CIRCLES

    RS AGGARWAL|Exercise EXERCISE 12C|26 Videos

  • CIRCLES

    RS AGGARWAL|Exercise MULTIPLE CHOICE QUESTION(MCQ)|37 Videos

  • BAR GRAPH, HISTOGRAM AND FREQUENCY POLYGON

    RS AGGARWAL|Exercise EXERCISE 17B|16 Videos

  • CONGRUENCE OF TRIANGLES AND INEQUALITIES IN A TRIANGLE

    RS AGGARWAL|Exercise Multiple Choice Questions (Mcq)|20 Videos

Similar Questions

Explore conceptually related problems

If the diameter of circle bisects each of the two chords of the circle, then both the chords: यदि वृत्त का व्यास वृत्त के दो जीवा को बराबर हिस्सों में काटता है, तो दोनों जीवा:

Prove that, if a diameter of a circle bisects two chords of the circle then those two chords are parallel to each other.

If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.

Is every diameter of a circle also a chord?

A diameter of a circle is a chord that………the centre.

Prove that a diameter of a circle which bisects a chord of the circle also bisects the angle subtended by the chord at the centre of the circle.

Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A.

DIAMETER A chord passing through the centre of a circle is known as its diameter. Note that a circle has many diameters and a diameter of a given circle is one of the largest chords of the circle.Also all diameters are of the same length.

(a) Is every diameter of a circle also a chord? (b) Is every chord of a circle also a diameter?

Show that if two chords of a circle bisect one another they must be diameters.

RS AGGARWAL-CIRCLES -Exercise 12A
  1. A chord of length 30cm is drawn at a distance of 8 cm from the centre ...

    Text Solution

    |

  2. In a circle of radius 5 cm, AB and CD are two parallel chords of lengt...

    Text Solution

    |

  3. Two parallel chords of lengths 30cm and 16cm are drawn on the opposite...

    Text Solution

    |

  4. In the given figure, CD is the diameter of a circle with centre O and...

    Text Solution

    |

  5. In the given figure, a circle with centre O is given in which a diamet...

    Text Solution

    |

  6. In the adjoining figure,OD is perpendicular to the chord AB of a circl...

    Text Solution

    |

  7. In the given figure, O is the centre of a circle in which chords AB an...

    Text Solution

    |

  8. Theorem :-2 The perpendicular from centre of a circle to the chord bis...

    Text Solution

    |

  9. Prove that two different circles cannot intersect each other at mor...

    Text Solution

    |

  10. Two circles of radii 10 cm and 8 cm intersect each other, and the leng...

    Text Solution

    |

  11. Two equal circles intersect in P and Q. A straight line through P meet...

    Text Solution

    |

  12. If a diameter of a circle bisects each of the two chords of a circl...

    Text Solution

    |

  13. AB is the chord of a circle with centreO. AB is produced to C, such th...

    Text Solution

    |

  14. AB and AC are two chords of a circle of radius r such that AB=2AC. If ...

    Text Solution

    |

  15. In the adjoining figure, O is the centre of a circle. If AB and AC are...

    Text Solution

    |

  16. In the adjoining figure, BC is a diameter of a circle with centre O. I...

    Text Solution

    |

  17. An equilateral triangle of side 9 cm is inscribed in a circle. Find...

    Text Solution

    |

  18. In the adjoining figure, AB and AC are two equal chords of a circle wi...

    Text Solution

    |

  19. In the adjoining figure, OPQR is a square. A circle drawn with centre ...

    Text Solution

    |

  20. Two circles whose centres are O and O ' intersect at Pdot Throug...

    Text Solution

    |