The figure shows two concentric circles and $AD$ is a chord of larger circle. prove that $AB=CD$.

In the following figure, $OABC$ is a square. A circle is drawn with $O$ as centre which meets $OC\text{ at }P\text{ and }OA\text{ at }Q$. Prove that : $∆OPA\cong ∆OQC$.

In the following figure, $OABC$ is a square. A circle is drawn with $O$ as centre which meets $OC\text{ at }P\text{ and }OA\text{ at }Q$. Prove that : $∆BPC\cong ∆BQA$.

The length of the common chord of two intersecting circles is $30$ cm. If the diameters of these two circles be $50$ cm and $34$ cm, calculate the distance between their centres.

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

In the given figure, a square is inscribed in a circle with centre $0$. Find $\angle COD$

In the given figure, $AB$ is a side of regular pentagon and $BC$ is a side of regular hexagon. Find $\angle OBC$.