The picutre on the right shows two circles centred on the same point and the line intersecting them.Prove that the parts of the line between the circles on either side are equal.

The picture on the right 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.

In the picture on the right, the angles between the radii and the chords are equal.Prove that the chords are of the same length.

The picture shows two circles with the same centre and two triangles formed by joining the centre to the points of intersection of the circles with two radii of the larger circle. prove that these triangles are similar .

The picture shows the tangents at two points on a circle and the radii through the points of contact. Prove that the tangents have the same length.

In the picture below, two lines are drawn from the top vertex of a triangle to the bottom side: Prove that the ratio in which these lines divide the length of the bottom side is equal to the ratio of the area of the three smaller triangles in the picture.

At two ends of a horizontal line, angles of equal size are drawn, and two points on the slanted lines are joined. Prove that the parts of the horizontal line and parts of slanted lines are in the same ratio.

In the picture below, two vertices of a parallelogram are joined to the mid points of two sides. Prove that these lines divides the diagonal in the picture into three equal parts. .

Prove that chords of the same length in a circle are at the same distance from the centre.

The lines joining the circumcentre of a Wangle to the vertices are extended to meet another circle with the same centre, and these points are joined to make another triangle. Prove that the two triangles are similar. .

Two chords intersect at a point on a circle and the diameter through this point bisects the angle between the chords. Prove that the chords have the same length.