Equal chords of a circle subtend equal angles at the centre and (motivate) its converse. The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.There is one and only one circle passing through three given non-collinear points. Equal chords of a circle (or of congruent circles) are equidistant from the center(s) and conversely.

9.G.C.3

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. Angles in the same segment of a circle are equal. if a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle. The sum of the either pair of the opposite angles of a cyclic quadrilateral is 180 degree and its converse.

Proofs and Theorems involving Circles

Interactive practice questions

Outcomes

9.G.C.2

9.G.C.3

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