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.

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.

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

A chord and the diameter through one of its ends are drawnin a circle. A chord of the same inclination is drawn on the other side of the diameter. Prove that the chords are of the same length.

In this picture the horizontal lines at the top and bottom are parallel. Prove that the yellow and red triangles are of the same area.

In this picture the horizontal lines at the top and bottom are parallel. Prove that the yellow and red triangles are of the same area.

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.

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.

In the two pictures below, the squares are of the same size. Prove that the green regions are of the same area.

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.

Two parallel chords in a circle of diameter 30 cm have lengths 24cm and 18 .cm If the chords are on the same side of the centre, what is the distance between them? If the chords are on either side-of the centre, what is the difference between them?