The line joining the mid-points of two chords of a circle passes through its center. Prove that the chords are parallel.

In the following figure, the line ABCD is perpendicular to PQ; where P and Q are the centers of the circles. Show that :

(i) AB = CD

(ii) AC = BD

In the given figure, O is center of the circle and ∠COD is greater than ∠AOB, then :

1. AB > CD

2. AB < CD

3. AB = CD

4. AB + CD = AD

In a circle, O is its center and AB, CD are its two chords. If AB : CD = 3 : 2, then ratio between ∠AOB and ∠COD is :

1. 1 : 1

2. 3 : 2

3. 2 : 5

4. 3 : 5