NCERT Solutions for Class 9 Maths Chapter 10 Circles

Short Note:

• Equal chords of a circle subtend equal angles at the centre, and conversely.

• The perpendicular from the centre of a circle to a chord bisects the chord, and the line joining the centre to the mid-point of a chord is perpendicular to the chord.

• Equal chords of a circle (or of congruent circles) are equidistant from the centre, and conversely.

Short Note:

• 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.

• The angle in a semicircle is a right angle.

Short Note:

• A quadrilateral whose all four vertices lie on a circle is a cyclic quadrilateral.

• The sum of either pair of opposite angles of a cyclic quadrilateral is 180°, and conversely, if the sum of a pair of opposite angles of a quadrilateral is 180°, it is cyclic.