The length of the complete circle is called its ............

Two chords $AB$ and $AC$ of a circle subtend angles equal to $90^{\circ}$ and $150^{\circ}$,respectively,at the centre. Find $\angle BAC$,if $AB$ and $AC$ lie on the opposite sides of the centre.

In the figure,$AOB$ is a diameter of the circle and $C, D, E$ are any three points on the semi-circle. Find the value of $\angle ACD + \angle BED$.

$AB$ and $CD$ are two parallel chords of a circle with centre $P$. Also,the centre $P$ lies between the chords $AB$ and $CD$. If $AB = 20\,cm$,$CD = 48\,cm$,and the radius of the circle is $26\,cm$,find the distance between $AB$ and $CD$.

$AB$ and $CD$ are two chords of a circle with centre $P$. The distance of chord $AB$ from the centre $P$ is $15 \, cm$ and the distance of chord $CD$ from the centre $P$ is $8 \, cm$. If $AB = 16 \, cm$,then find the length of chord $CD$. (in $, cm$)

In the figure,$\angle AOB = 90^{\circ}$ and $\angle ABC = 30^{\circ},$ then $\angle CAO$ is equal to: (in $^{\circ}$)