| 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. |