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

If two chords $AB$ and $CD$ of a circle intersect at right angles (see Fig.),prove that $\text{arc } CXA + \text{arc } DZB = \text{arc } AYD + \text{arc } BWC = \text{semicircle}$.

$XY$ is a diameter of the circumcircle of $\Delta XYZ$. What is the value of $\angle XZY$ (in $^{\circ}$)?

State whether the following statement is True or False and justify your answer: $ABCD$ is a cyclic quadrilateral such that $\angle A = 90^{\circ}, \angle B = 70^{\circ}, \angle C = 95^{\circ}$ and $\angle D = 105^{\circ}$.

$ABCD$ 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 $^{\circ}$)