Home
Class 9
MATHS
In Figure, A B is a diameter of a cir...

In Figure, `A B` is a diameter of a circle `C(O ,\ r)dot` Chord `C D` is equal to radius `O Cdot` If `A C\ a n d\ B D` when produced intersect at `P ,` prove that `/_A P B` is constant.

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 Figure, A B is a diameter of the circle such that /_A=35^0a n d\ /_Q=25^0, find /_P B R

In Figure, A B C D is a parallelogram in which P is the mid-point of D C\ a n d\ Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C\ a t\ R , prove that R is a mid-point of B C

In Figure, A B C D is a parallelogram in which P is the mid-point of D C and Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C at Rdot Prove that R is a mid-point of B Cdot

In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respectively. The altitude A P\ to\ B C intersects F E\ at Qdot Prove that A Q=Q P

In Figure, A B C D is a parallelogram and /_D A B=60^0dot If the bisectors A P\ a n d\ B P of angles A\ a n d\ B respectively, meet at P on C D , prove that P is the mid-point of C D

P is the mid-point of side A B of a parallelogram A B C D . A line through B parallel to P D meets D C at Q\ a n d\ A D produced at Rdot Prove that: A R=2B C (ii) B R=2\ B Q

In Figure, A B C D is a trapezium in which A B||C D . Prove that: a r( A O D)=a r( B O C)dot

In Figure, B E_|_A C ,\ A D is any line from A\ to\ B C intersecting B E in HdotP ,\ Q\ a n d\ R are respectively the mid-points of A H ,\ A B\ a n d\ B Cdot Prove that /_P Q R=90^0

A B C D is a parallelogram. A D is a produced to E so that D E=D C and E C produced meets A B produced in Fdot Prove that B F=B Cdot

RD SHARMA-CIRCLE -All Questions
  1. In an isosceles triangle A B C with A B=A C , a circle passing thr...

    Text Solution

    |

  2. In Figure, /A=60^0\ a n d\ /A B C=80^0, find /D P C\ a n d\ /B Q C

    Text Solution

    |

  3. In Figure, A B is a diameter of a circle C(O ,\ r)dot Chord C D is ...

    Text Solution

    |

  4. P Q\ a n d\ R S are two parallel chords of a circle and lines R P\ a...

    Text Solution

    |

  5. A B C D is a cyclic quadrilateral whose diagonals A C\ a n d\ B D in...

    Text Solution

    |

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

    Text Solution

    |

  7. A B C is a triangle in which A B=A C\ a n d\ P is a point on A C ....

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. In Figure, A B C is an equilateral triangle. Find m\ /B E C

    Text Solution

    |

  11. In Figure, P Q R is an isosceles triangle with P Q=P R\ a n d\ m/P...

    Text Solution

    |

  12. In Figure, O is the centre of the circle. If /B O D=160^0, find the ...

    Text Solution

    |

  13. In Figure A B C D is a cyclic quadrilateral. If /B C D=100^0a n d\ /A ...

    Text Solution

    |

  14. If A B C D is a cyclic quadrilateral in which AD|\|BC . Prove that /...

    Text Solution

    |

  15. In Figure, O is the centre of the circle. Find /C B D

    Text Solution

    |

  16. A B\ a n d\ C D are diameters of a circle with centre Odot If /O B D...

    Text Solution

    |

  17. On a semi-circle with A B as diameter, a point C is taken, so th...

    Text Solution

    |

  18. In a cyclic quadrilateral A B C D, if AB |\| CD\ a n d\ /B=70^@, fin...

    Text Solution

    |

  19. In a cyclic quadrilateral A B C D , if /A=3 /C). Find /A

    Text Solution

    |

  20. In Figure, O is the centre of the circle and /D A B=50^0dot Calculat...

    Text Solution

    |