# NCERT Class 9 Maths Formula CBSE Board Sample Problems Part 10

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## 10. Circles

1. | A circle is a collection of all the points in a plane, which are equidistant from a fixed point in the plane |

2. | Equal chords of a circle (or of congruent circles) subtend equal angles at the center. |

3. | If the angles subtended by two chords of a circle (or of congruent circles) at the center (corresponding center) are equal, the chords are equal. |

4. | The perpendicular from the center of a circle to a chord bisects the chord. |

5. | The line drawn through the center of a circle to bisect a chord is perpendicular to the chord. |

6. | There is one and only one circle passing through three non-collinear points |

7. | Equal chords of a circle (or of congruent circles) are equidistant from the center (or corresponding centers). |

8. | Chords equidistant from the center (or corresponding centers) of a circle (or of congruent circles) are equal |

9. | If two arcs of a circle are congruent, then their corresponding chords are equal and conversely, if two chords of a circle are equal, then their corresponding arcs (minor, major) are congruent. |

10. | Congruent arcs of a circle subtend equal angles at the center. |

11. | The angle subtended by an arc at the center ¡s double the angle subtended by it at any point on the remaining part of the circle |

12. | Angles in the same segment of a circle are equal |

13. | AngIe in a semicircle is a right angle. |

14. | If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle. |

15. | The sum of either pair of opposite angles of a cyclic quadrilateral is |

16. | If the sum of a pair of opposite angles of a quadrilateral is 180°, then the quadrilateral is cyclic. |