Home
Class 9
MATHS
A B C is a triangle in which A B=A C\ ...

`A B C` is a triangle in which `A B=A C\ a n d\ P` is a point on `A C` . Through `C` a line is drawn to intersect `B P` produced at `Q` such that `/_A B Q=\ /_A C Q`. Prove that: `/_A Q C=90^@+1/2/_B A C`

Promotional Banner

Topper's Solved these Questions

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    RD SHARMA ENGLISH|Exercise All Questions|206 Videos

  • CONGRUENT TRIANGLE

    RD SHARMA ENGLISH|Exercise All Questions|290 Videos

Similar Questions

Explore conceptually related problems

If A B C D is a quadrilateral in which A B C D and A D=B C , prove that /_A = /_B .

A B C is a triangle, P is a point on A B a n dQ is a point on A C such that /_A Q P=/_A B Cdot Complete the relation (A r e aof A P Q)/(A r e aof A B C)=dot(())/(A C^2) .

A B C is a triangle right angled at B ; a n d\ P is the mid-point of A C . Prove that: P Q\ _|_A B (ii) Q is the mid point of A B P B=P A=1/2A C

In a triangle A B C , if A B=A C\ a n d\ A B is produced to D such that B D=B C , find /_A C D\ :\ /_A D C

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 Q . Prove that A Q=Q P .

Two circle with centres A and B intersect at C and Ddot Prove that /_A C B=/_A D Bdot

In a \ A B C ,\ A D bisects /_A\ a n d\ /_C >/_Bdot Prove that /_A D B >\ /_A D C .

In a triangle A B C , N is a point on A C such that B N_|_A C . If B N^2=A N N C , prove that /_B=90o .

Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig. 10.40). Prove that /_A C P\ =/_Q C D .

Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Figure). Prove that /_A C P=/_Q C D .

RD SHARMA ENGLISH-CIRCLE -All Questions
  1. A B C D is a cyclic quadrilateral whose diagonals A C\ a n d\ B D in...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. In any triangle ABC, if the angle bisector of /A and perpendicular bi...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. If A B C D is a cyclic quadrilateral in which A D || B C . Prove tha...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. In a cyclic quadrilateral A B C D, if AB || CD\ a n d\ /B=70^0, find...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. In Figure, if /B A C=60^0\ a n d\ /B C A=20^0,\ find /A D C

    Text Solution

    |

  17. In Figure, if A B C is an equilateral triangle. Find /B D C\ a n d\...

    Text Solution

    |

  18. In Figure, O is the centre of the circle. If /C E A=30^0, find the ...

    Text Solution

    |

  19. In Figure, /B A D=78^0,\ /D C F=x^0a n d\ /D E F=y^0dot Find the va...

    Text Solution

    |

  20. In a cyclic quadrilateral A B C D , if /A-\ /C=60^0, prove that ...

    Text Solution

    |