Question

Theorems of 9th class circles.

Answer 1

1. Equal chords of a circle subtend equal angles at the centre.
2.If the angles subtended by the chords at the centre are equal then the chords are equal.
3.The perpendicular drawn from the centre of a circle to a chord bisects the chord.
4.If the line drawn from centre of a circle bisects the chord the line is perpendicular to chord.
5.There is one and only one circle passing through three given non-collinear points.
6.Equal chords of a circle are equidistant from the centre.
7.Chords equidistant from the centre are equal in length.
8.The angle subtended by an arc at the centre is double the angle subtended by it at any part of the remaining circle.
9.Angles in the same segment are equal.
10.If a pine segment joining two points subtends equal angles at two other parts lying on the same side of the line containing the line segment the four points lie on the circle.
11.The sum of either pair of opposite angles of a cyclic quadrilateral is 180°.
12.If the sum of a pair of opposite angles of a quadrilateral is 180° the quadrilateral is cyclic.