A chord of length $24$ cm is at a distance of $5$ cm from the centre of the circle. Find the length of the chord of the same circle which is at a distance of $12$ cm from the 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.

Two parallel chords are drawn in a circle of diameter $30$ cm. The length of one chord is $24$ cm and the distance between the two chords is $21$ cm; find the length of the other chord.

A chord $CD$ of a circle whose centre is $O$ is bisected at $P$ by a diameter $AB$. Given $OA=OB=15 \text{cm} \text{ and }OP=9$ cm. Calculate the length of $CD$.

A chord $CD$ of a circle whose centre is $O$ is bisected at $P$ by a diameter $AB$. Given $OA=OB=15 \text{cm} \text{ and }OP=9$ cm. Calculate the length of $CB$.

A chord $CD$ of a circle whose centre is $O$ is bisected at $P$ by a diameter $AB$. Given $OA=OB=15 \text{cm} \text{ and }OP=9$ cm. Calculate the length of $AD$.

The figure, given below, shows a circle with centre $O$ in which diameter $AB$ bisects the chord $CD$ at point $E$. If $CE = ED =8$ cm and $EB=4$ cm, find the radius of the circle.