In the figure,$\angle PQR = 100^{\circ}$,where $P, Q$ and $R$ are points on a circle with centre $O$. Find $\angle OPR$. (in $^{\circ}$)

$A$ circular park of radius $20 \, m$ is situated in a colony. Three boys Ankur,Syed and David are sitting at equal distances on its boundary,each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone.

In the figure,$AB$ is a diameter of the circle,and $CD$ is a chord equal to the radius of the circle. $AC$ and $BD$ when extended intersect at a point $E$. Prove that $\angle AEB = 60^{\circ}$.

Two congruent circles intersect each other at points $A$ and $B$. Through $A$,any line segment $PAQ$ is drawn such that $P$ and $Q$ lie on the two circles. Prove that $BP = BQ$.

$A$ chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in the major segment.

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