In quadrilateral $ABCD$,if $\angle A : \angle B : \angle C : \angle D = 3 : 2 : 4 : 5$,then identify the type of quadrilateral $ABCD$.

In the figure,if $AOB$ is a diameter of the circle and $AC = BC$,then $\angle CAB$ is equal to (in $^{\circ}$)

In the figure,$\angle ACB = 40^{\circ}$. Find $\angle OAB$.

$ABCD$ is a cyclic quadrilateral. If $AB \parallel CD$,then prove that $BC = AD$.

$AB$ and $CD$ are two parallel chords of a circle with centre $P$. Also,the centre $P$ lies between $AB$ and $CD$. If $AB = 48 \, cm$,$CD = 40 \, cm$,and the radius of the circle is $25 \, cm$,find the distance between $AB$ and $CD$. (in $, cm$)

$AB$ 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 $CD$.