Kerala Board Solutions for Chapter: Circles, Exercise 1: Exercise 1

Prove that the line joining the centres of two intersecting circles is the perpendicular bisector of the line joining the points of intersection.

The picture given below, shows two circles centred on the same point and a line intersecting them. Prove that the parts of the line between the circles on either side are equal.

The figure given below, shows two chords drawn on either sides of a diameter. What is the length of the other chord? (in cm)

A chord and the diameter through one of its ends are drawn in a circle. A chord of the same inclination is drawn on the other side of the diameter, as given below,

Prove that the chords are of the same length.

The figure shows two chords drawn on either sides of a diameter. How much is the angle the other chord makes with the diameter?

Prove that the angle made by two equal chords drawn from a point on the circle is bisected by the diameter through that point.

Draw a square and a circle through all four vertices. Draw diameters parallel to the sides of the square and draw a polygon joining the end points of these diameters and vertices of the square.

Prove that this polygon is a regular octagon.