In a circle with centre $P$,the chord $AB = 8 \, cm$ and the radius $= 8 \, cm$. Then,$\angle APB = \dots$ (in $^{\circ}$)

In a circle with centre $P$,$AB$ is a chord and point $C$ is a point other than $A$ and $B$ on the major arc $AB$. If $\angle ACB + \angle APB = 150^{\circ}$,then find $\angle APB$. (in $^{\circ}$)

In the figure,$OD$ is perpendicular to chord $AB$ of a circle whose centre is $O.$ If $BC$ is a diameter,prove that $CA = 2OD$.

Three girls Reshma,Salma and Mandip are playing a game by standing on a circle of radius $5 \, m$ drawn in a park. Reshma throws a ball to Salma,Salma to Mandip,Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is $6 \, m$ each,what is the distance between Reshma and Mandip?

$A$ piece of a circle between two points on a circle is called ........ of the circle.

If arcs $AXB$ and $CYD$ of a circle are congruent,find the ratio of $AB$ and $CD.$