# NCERT Class 10 Mathematics Formula CBSE Board Sample Problems Part 7

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## Area of Circles

S.no | Points |

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 is 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 | Angle 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. |

S.no | Terms | Description |

1 | Circumference of a circle | |

2 | Area of circle | |

3 | Length of the arc of the sector of angle | Length of the arc of the sector of angle |

4 | Area of the sector of angle | Area of the sector of angle |

5 | Area of segment of a circle | Area of the corresponding sector — Area of the corresponding triangle |