Home
Class 9
MATHS
Prove that the angle in a segment grea...

Prove that the angle in a segment greater than a semi-circle is less than a right angle.

Text Solution

Verified by Experts

Join `OA \and\ AB`
`arc ADB` subtends `/_AOB` at the centre
`/_ACB`at the remaining part of the circle.
`/_ACB=1/2/_AOB`
`/_AOB<180^0` (A straight angle)
`/_ACB<1/2xx180^0`
`/_ACB<90^0`
Hence ,`/_ACB<90^0`
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

The angle in a semi-circle is a right angle.

The angle in a semi-circle is a right angle

Using vector method,prove that the angel in a semi circle is a right angle.

Prove that an angle inscribed in a semi-circle is a right angle using vector method.

Prove that the sum of the angles in the four segments exterior to a cyclic quadrilateral is equal to 6 right angles.

In the given figure, angle a is greater than one-sixth of right angle, then.

What a ray of light passes from air into glass, is the angle of refraction greater than or less than the angle of incidence?

Find the angles when the angles are complementary and the smaller is 40^@ less than the larger

RD SHARMA-CIRCLE -All Questions
  1. If the two sides of a pair of opposite sides of a cyclic quadrilater...

    Text Solution

    |

  2. A B C D is a cyclic quadrilateral in which B A\ a n d\ C D when pr...

    Text Solution

    |

  3. Prove that the angle in a segment greater than a semi-circle is less...

    Text Solution

    |

  4. A B C D is a cyclic trapezium with A D B Cdot If /B=70^0, determine...

    Text Solution

    |

  5. Prove that the line segment joining the mid-point of the hypotenuse ...

    Text Solution

    |

  6. A B C D is a cyclic quadrilateral in which A C\ a n d\ B D are its d...

    Text Solution

    |

  7. In Figure, two circles intersect at A\ a n d\ B . The centre of th...

    Text Solution

    |

  8. In Figure, two congruent circles with centers O\ a n d\ O ' intersec...

    Text Solution

    |

  9. A B C D is a cyclic quadrilateral in which /B A D=75^0,\ /A B D=58^0...

    Text Solution

    |

  10. In Figure, if /A O B=80^0a n d\ /A B C=30^0, then find /C A O

    Text Solution

    |

  11. If O is the circumcentre of A B C , then find the value of /O B C...

    Text Solution

    |

  12. If Figure, A O C is a diameter of the circle and are A X B=1/2 arc B...

    Text Solution

    |

  13. In Figure, A is the centre of the circle. A B C D is a parallelogram...

    Text Solution

    |

  14. In Figure, A B is a diameter of the circle such that /A=35^0a n d\ /...

    Text Solution

    |

  15. In Figure, P\ a n d\ Q are centres of two circles intersecting at B\...

    Text Solution

    |

  16. In Figure, A B C D is quadrilateral inscribed in a circle with centr...

    Text Solution

    |

  17. If the length of a chord of a circle is 16 cm and is at a distance o...

    Text Solution

    |

  18. The radius of a circle is 6 cm. The perpendicular distance from the ...

    Text Solution

    |

  19. If O is the centre of a circle with radius r and AB is a chord of the ...

    Text Solution

    |

  20. A B C D is a cyclic quadrilateral such that /A D B=30^0a n d\ /D C A...

    Text Solution

    |