1.In the figure, OD is perpendicular to chord AB of a circle whose centre is O. If BC is diameter; prove that CA = 2OD.
2. l is a line intersecting two concentric circles having common centre O, at A, B, C and D. Prove that AB = CD.
3. AB and CD are equal chords of a circle whose centre is O. When produced, these chords meet at E. Prove that EB = ED.
4. If O be the centre of the circle, find the value of ï¿½xï¿½ in each of the following figures.
5. Prove that equal chords of a circle subtend equal angles at the centre.
6. The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. Prove it.
7. Prove that equal chords of a circle (or congruent circles) are equidistant from the centre (or centres).
8. In the figure, OD is perpendicular to the chord AB of a circle with centre O. If BC is a diameter, show that AC || OD and AC = 20D.
Hint: ∴ OD ⊥ AB therefore; D is the mid-point of AB.
9. If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal.
10. Show that the angles in the same segment of a circle are equal.