Prove that equal chords of congruent circles subtend equal angles at their centre.

In the following figure, $AD$ is a straight line. $OP\perp AD$ and $O$ is the centre of both circles. If $OA=34 \text{cm},OB=20\text{cm} \text{and} OP=16 \text{cm}$; find the length of $AB$.

In a circle of radius $17$ cm, two parallel chords of lengths $30 \text{cm and }16 \text{cm}$ are drawn. Find the distance between the chords, if both the chords are on the opposite sides of the centre.

In a circle of radius $17$ cm, two parallel chords of lengths $30 \text{cm and }16 \text{cm}$ are drawn. Find the distance between the chords, if both the chords are on the same side of the centre.