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.

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.

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 the tangents at two points on a circle and the radii through the points of contact. Prove that the tangents 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.

If the length of a chord of a circle of diameter 40 cm is 20 cm , what is the angle subtended by the chord at the centre of the circle ?

In a circle of radius 5 cm two parallel chords of lengths 6cm and 8 cm are drawn on either sides of a diam¬eter. What is the distance between them? If parallel chords of these lengths are drawn on the same side of a diameter what would be the distance between them.

In a circle of radius 25 centimetres, the lengths of two parallel chord's are 30cm and 40 cm. If the chords are on the same side of the diameter, what is the distance between? If the chords are on either of the diameter, what is the distance between them?

How many chords can be drawn through 12 point on a circle?

How many chords can be drawn through 15 points on a circle?

How many chords can be drawn through 20 points on a circle?