Home
Class 9
MATHS
In the Figure, O D is perpendicular to ...

In the Figure, `O D` is perpendicular to the chord `A B` of a circle whose centre is `Odot` If `B C` is a diameter, show that `C A=2 OD`

Text Solution

Verified by Experts

`OD_|_AB`
D is mid point of AB
BC is diameter
O is the midpoint of BC
BD=`1/2`AC
AC=2*DB.
Promotional Banner

Topper's Solved these Questions

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    RD SHARMA|Exercise All Questions|205 Videos

  • CONGRUENT TRIANGLE

    RD SHARMA|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

In the figure,OD is perpendicular to the chord AB of a circle whose centre is O .If BC is a diameter,show that CA=2OD

In a circle OD is perpendicular to chord AB of a circle with centre O.If BC is a diameter then the AC/OD is:

In Figure,OA and OB ar respectively perpendiculars to chords CD and EF of a circle whose centre is O. If OA=OB, prove that CE=DF.

In the given figure, AB and PQ are perpendicular diameters of the circle whose centre is O and radius OA = 7 cm. Find the area of the shade region.

In the given figure, O is the centre of the circle. Name all chords of the circle.

In the given figure,AB and AC are two equal chords of a circle with centre O.Show that o lies on the bisectors of /_BAC.

In Figure,AB and AC are two equal chords of a circle whose centre is O .If OD perp AB and OE perp AC, prove that ADE is an isosceles triangle.

In Figure,l is a line intersecting the two concentric circles,whose common centre is O, at the points A,B,C and D. Show that AB=CD

In Figure,l is a line intersecting the two concentric circles,whose common centre is O, at the points A,B,C and D. Show that AB=CD

The greatest chord of a circle is called its radius (b) secant (c) diameter (d) none of these

RD SHARMA-CIRCLE -All Questions
  1. In an equilateral triangle, prove that the centroid and the circumcent...

    Text Solution

    |

  2. In Figure, l is a line intersecting the two concentric circles, whose ...

    Text Solution

    |

  3. In the Figure, O D is perpendicular to the chord A B of a circle who...

    Text Solution

    |

  4. AB and CD are two chords of a circle such that AB = 6 cm, CD = 12 cm a...

    Text Solution

    |

  5. A B and C D are two parallel chords of a circle such that A B=10c m an...

    Text Solution

    |

  6. P Q and R S are two parallel chords of a circle whose centre is O and ...

    Text Solution

    |

  7. A B and C D are two parallel chords of a circle whose diameter is A C ...

    Text Solution

    |

  8. If a diameter of a circle bisects each of the two chords of a circle, ...

    Text Solution

    |

  9. Prove that the line joining the midpoints of any two sides of a triang...

    Text Solution

    |

  10. Prove that the angle in a segment greater than a semi-circle is les...

    Text Solution

    |

  11. Prove that the angle in a segment greater than a semi-circle is les...

    Text Solution

    |

  12. A B C D is a parallelogram. A B is produced to E so that B E=A B . Pro...

    Text Solution

    |

  13. If two sides of a cyclic quadrilateral are parallel, prove that the ...

    Text Solution

    |

  14. Prove that the circle drawn with any side of a rhombus as a diameter,p...

    Text Solution

    |

  15. Let the vertex of an angle ABC be located outside a circle and let the...

    Text Solution

    |

  16. In any triangle ABC, if the angle bisector of /Aand perpendicular bis...

    Text Solution

    |

  17. P is a point on the side B C of a triangle A B C such that A B=A Pdot ...

    Text Solution

    |

  18. A B C D is a cyclic quadrilateral whose diagonals A Ca n dB D intersec...

    Text Solution

    |

  19. (Converse of Theorem 3) The line joining the centre of a circle to the...

    Text Solution

    |

  20. .The equation of the circle passing through three non-collinear points...

    Text Solution

    |