In the figure,if $\angle ABC = 20^{\circ},$ then $\angle AOC$ is equal to (in $^{\circ}$)

In a circle with centre $P$,the distance of a chord $AB$ from the centre $P$ is $20 \, cm$. If $AB = 96 \, cm$,then the radius of the circle is .......... $cm$.

$AB$ and $CD$ are two parallel chords of a circle with centre $P$. Centre $P$ is not between the two chords $AB$ and $CD$. If $AB = 40\,cm$,$CD = 30\,cm$ and the radius of the circle is $25\,cm$,find the distance between $AB$ and $CD$. (in $,cm$)

$P$ is the centre of the circle of radius $20\, cm$. $AB$ is a chord of the circle. If $AB = 32\, cm$,then find the distance of the chord $AB$ from the centre $P$.

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?

In cyclic quadrilateral $PQRS$,if $5 \angle Q = 7 \angle S$,then find the value of $\angle Q$. (in $^{\circ}$)