Summary

In this chapter, you have studied the following points:

1. A circle is the collection of all points in a plane, which are equidistant from a fixed pointline in the plane.

2. Equal chords of a circle (or of congruent circles) subtend equal anglesline segments at the centre.

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

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

5. The line drawn through the centre of a circle to bisect a chord is perpendicularlinear to the chord.

6. Equal chords of a circle (or of congruent circles) are equidistantequal from the centre (or corresponding centres).

7. Chords equidistant from the centre (or corresponding centres) of a circle (or of congruent circles) are .

8. If two arcs of a circle are congruent, then their corresponding chords are and conversely if two chords of a circle are equal, then their corresponding arcs (minor, major) are congruenttwice the length.

9. Congruent arcs of a circle subtend equal anglessecants at the centre.

10. The angle subtended by an arc at the centre is doublethrice the angle subtended by it at any point on the remaining part of the circle.

11. Angles in the same segment of a circle are .

12. Angle in a semicircle is a rightstraight angle.

13. 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 circlesemi-circle.

14. The sum of either pair of opposite angles of a cyclic quadrilateral is °.

15. If sum of a pair of opposite angles of a quadrilateral is ° , the quadrilateral is cyclic.