$ABCD$ is a cyclic quadrilateral in which $\angle A = 80^{\circ}$ and $\angle B = 75^{\circ},$ then $\angle D = \dots$ (in $^{\circ}$)

Two circles of radii $8 \ cm$ with centers $P$ and $Q$ are given. The chord $AB$ of the circle with center $P$ and the chord $CD$ of the circle with center $Q$ are equal. If $\angle PAB = 40^{\circ}$,then find $\angle CQD$. (in $^{\circ}$)

$A, B$ and $C$ are three points on a circle. Prove that the perpendicular bisectors of $AB, BC$ and $CA$ are concurrent.

In a circle with centre $P$,$AB$ and $CD$ are equal chords. If $\angle APB = 80^{\circ},$ then $\angle CPD =$ .......... (in $^{\circ}$)

The chord which passes through the centre of the circle is called a .......... of the circle.

In a circle with centre $P$,$AB$ is a diameter and point $C$ is a point other than $A$ and $B$. If the radius of the circle is $34 \, cm$ and $AC = 32 \, cm$,then $BC = $ .......... $cm$.