Home
Class 9
MATHS
D\ a n d\ E are, respectively, the po...

`D\ a n d\ E` are, respectively, the points on equal sides `A B\ a n d\ A C` of an isosceles triangle `A B C` such that `B ,\ C ,\ E ,\ a n d\ D` are concyclic as shown in Figure. If `O` is the point of intersection of `C D\ a n d\ B E ,` prove that `A O` is the bisector of line segment `D E`

Text Solution

AI Generated Solution

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

D and E are points on equal sides A B and A C of an isosceles triangle A B C such that A D=A E . Prove that B ,C ,D ,E are concylic.

In Figure, if A B=A C\ a n d\ B E=C D , prove that A D=A Edot

In Figure, A B=C D . Prove that B E=D E\ a n d\ A E=C E , where E is the point of intersecting of A D\ a n d\ B C .

In Figure, A D\ a n d\ B E are respectively altitudes of an isosceles triangle A B C with A C=B Cdot Prove that A E=B D

In an isosceles triangle A B C with A B=A C , a circle passing through B\ a n d\ C intersects the sides A B\ a n d\ A C at D\ a n d\ E respectively. Prove that D E || B C .

B D\ a n d\ C E are bisectors of /_B\ a n d\ /_C of an isosceles A B C with A B=A C . Prove that B D=C E

If D and E are points on sides A B and A C respectively of a triangle A B C such that D E || B C and B D=C E . Prove that A B C is isosceles.

In Figure, A E bisects /_C A D\ a n d\ /_B=/_Cdot Prove that A E||B C

A D\ a n d\ B E are respectively altitudes of A B C such that A E=B D . Prove that A D=B E .

In Figure, A B C is an isosceles triangle with A B=A C ,\ B D\ a n d\ C E are two medians of the triangle. Prove that B D=C E

RD SHARMA ENGLISH-CIRCLE -All Questions
  1. A B C is an isosceles triangle in which A B=A Cdot If Da n dE are the ...

    Text Solution

    |

  2. D and E are points on equal sides A B and A C of an isosceles triangle...

    Text Solution

    |

  3. D\ a n d\ E are, respectively, the points on equal sides A B\ a n d...

    Text Solution

    |

  4. A B C D is a cyclic quadrilateral. A Ba n dD C are produced to meet in...

    Text Solution

    |

  5. In Figure, P Q R S is a cyclic quadrilateral. Find the measure of each...

    Text Solution

    |

  6. Prove that any cyclic parallelogram is a rectangle.

    Text Solution

    |

  7. A Ca n dB D are chords of a circle which bisect each other. Prove that...

    Text Solution

    |

  8. A B C D is a parallelogram. The circle through A ,Ba n dC intersects C...

    Text Solution

    |

  9. Fill in the blanks: All point lying inside/outside a circle are ...

    Text Solution

    |

  10. Write the truth value (T/F) of the following with suitable reasons:...

    Text Solution

    |

  11. The radius of a circle is 13 cm and the length of one of its chords...

    Text Solution

    |

  12. Find the length of a chord which is at a distance of 5 cm from the ...

    Text Solution

    |

  13. In Figure, O is the centre of the circle of radius 5\ c m. O P\ |A B...

    Text Solution

    |

  14. In Figure, O is the centre of the circle of radius 5\ c mdotO P|A B...

    Text Solution

    |

  15. P Q\ a n d\ R S are two parallel chords of a circle whose centre is...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. A B\ a n d\ C D are two chords of a circle such that A B=6\ c m ,\ C...

    Text Solution

    |

  19. In the figure, O D is perpendicular to the chord A B of a circle...

    Text Solution

    |

  20. In Figure, l is a line intersecting the two concentric circles, who...

    Text Solution

    |