Home
Class 9
MATHS
Any angle subtended by a minor arc in th...

Any angle subtended by a minor arc in the alternate segment is acute and any angle subtended by a major arc in the alternate segment is obtuse.

Text Solution

Verified by Experts

`2/_PRQ=m(PQ)=/_POQ`
`2/_PRQ<180^@`
`/_PRQ<90^@`
`/_PRQ` is an acute angle.
BP is major axis
2`/_PGQ`=reflex(POQ)
`2/_PSB>360^@-180^@`
`/_PSQ>90^@`
...
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

Theorem:-6Any angle subtended by minor arc in the alternate segment is acute and any angle subtended by major arc in the alternate segment is obtuse.

The angle subtended by a minor arc in its alternate segment is…………….

Theorem:-5(i) The degree measure of an arc or angle subtended by an arc at the centre is double the angle subtended by it at any point of alternate segment.(ii) Angle in the same segment of a circle are equal (iii) The angle in the semi circle is right angle.

Minor and major arcs

Which of the following can be the angle subtended by a minor arc at the centre?

The angle subtended by an arc of a circle at the centre is double the angle subtended by it any point on the remaining part of the circle.

Show that any angle in a semi-circle is a right angle. The following arc the steps involved in showing the above result. Arrange them in sequential order. A) therefore angleACB=180^(@)/2=90^(@) B) The angle subtended by an arc at the center is double of the angle subtended by the same arc at any point on the remaining part of the circle. c) Let AB be a diameter of a circle with center D and C be any point on the circle. Join AC and BC. D) therefore angleAD = 2 xx angleACB 180^(@)=2angleACB(therefore angleADB=180^(@))

Theorem 10.8 : The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

The chord of a circle is sqrt(3) times its radius. The angle subtended by this chord at the minor arc is k times the angle subtended at the major arc. What is the value of k ?

Consider the following statements 1. the opposite angles of a cyclic quadrilateral are supplementary. 2. Angle subtended by an arc at the centre is doubled the angle subtended by it any point on the remaining part of the circle. Which one of the following is correct in respect of the above statements

RD SHARMA-CIRCLE -All Questions
  1. Two circles are drawn with sides A B ,A C of a triangle A B C as diame...

    Text Solution

    |

  2. Two circle intersect in Aa n dBa n dA Ca n dA D are respectively the d...

    Text Solution

    |

  3. Any angle subtended by a minor arc in the alternate segment is acute ...

    Text Solution

    |

  4. The arc of a circle subtending a right angle at any point of the circl...

    Text Solution

    |

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

    Text Solution

    |

  6. Angle in the same segment of a circle are equal.

    Text Solution

    |

  7. Prove that the circle drawn on any one of the equal sides of an isos...

    Text Solution

    |

  8. A chord of a circle is equal to the radius of the circle find the angl...

    Text Solution

    |

  9. In Figure., A B C is a triangle in which /B A C=30^0dot Show that B C ...

    Text Solution

    |

  10. Theorem:-7 If the line segment joining two points subtends equal angle...

    Text Solution

    |

  11. In Figure, O A and O B ar respectively perpendiculars to chords C D an...

    Text Solution

    |

  12. Draw the graph of the fuction 4x+3y=12,at what pt it cut the coordinat...

    Text Solution

    |

  13. If two equal chords of a circle in intersect within the circle, prove ...

    Text Solution

    |

  14. prove that the line joining the mid-point of two equal chords of a c...

    Text Solution

    |

  15. Show that if two chords of a circle bisect one another they must be ...

    Text Solution

    |

  16. In Figure, equal chords A B and C D of a circle with centre O , cut at...

    Text Solution

    |

  17. Two equal circles intersect in P and Q . A straight line through P mee...

    Text Solution

    |

  18. Prove that all the chords of a circle through a given point within it,...

    Text Solution

    |

  19. Prove that the diameter is the greatest chord in a circle.

    Text Solution

    |

  20. Bisector A D of /B A C of A B C passes through the centre O of the ci...

    Text Solution

    |