In the adjoining figure $AB$ is a chord equal to the radius of the circle with centre $O$. Find the values of $x \text{and} y?$

In the adjoining figure, equal chords $AB$ and $CD$ intersect each other at $Q$ at right angles of a circle with centre $O.$ Show that $OPQR$ is a square.

In the adjoining figure, $O$ is the centre of circle and points $A,B,C$ lie on the circle. If $\angle AOB=25°$, then find the value of $x?$

In the adjoining figure, $O$ is the centre of circle. If $\angle BOD=140°,$ then find the value of $x?$

In the adjoining figure, $O$ is the centre of circle. If $\angle PQR=100°,$find $\angle OPR?$

In the adjoining figure, $ABC$ is an isosceles triangle with $AB=AC.$ If $\angle ABC=50°$, find $\angle BDC, \angle BEC.$

In the adjoining figure, $O$ is the centre of the circle. If $\angle BCD=130°$, then find $\angle DAB.$

In the adjoining figure, $O$ is the centre of the circle. If $\angle BCD=130°$, then find $\angle DBA.$