## Important rules of circle

__Points to Remember :-__

*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 centre.*

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

*4. The perpendicular from the centre of a circle to a chord bisects the chord.*

*5. The line drawn through the centre 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 centre (or corresponding centres).*

*8. Chords equidistant from the centre (or corresponding centres) 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 centre.*

*11. 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.*

*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 180°.*

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

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