In the given figure, XZ is a diameter and Wis the mid point
of XY. Show that XZ = ZY.

In the given figure, $O$ is the centre of the circle. If $\angle ABO=30°$, find $\angle AOB$, $\angle ADB$ and $\angle BDC$.

In the given figure, $△ABC$ is inscribed in a circle. The bisector of $\angle A$ meets the circle in $L$ and the bisector of $\angle C$ meets $AL$ at $K$. If $\angle BAC=80°$ and $\angle ACB=60°$, find $\angle LKC$ and $\angle LCK$.