Prove that a diameter of a circle, which bisects a chord of the circle, also bisects the angle subtended by the chord at the centre of the circle.

In the given figure, L and M are mid-points of two equal chords AB and CD of a circle with centre O. Prove that :

(i) ∠OLM = ∠OML

(ii) ∠ALM = ∠CML

In an equilateral triangle, prove that the centroid and the circumcentre of the triangle coincide.

If a chord is at a distance of 8 cm from the centre of the circle of radius 17 cm, then the length of the chord will be :

1. 15 cm

2. 20 cm

3. 30 cm

4. 45 cm