The tangent at a point $C$ of a circle and a diameter $AB$ when extended intersect at $P$. If $\angle PCA = 110^{\circ},$ find $\angle CBA$ [see $Fig.$]. (in $^{\circ}$)

At one end $A$ of a diameter $AB$ of a circle of radius $5 \, cm$,a tangent $XY$ is drawn to the circle. The length of the chord $CD$ parallel to $XY$ and at a distance of $8 \, cm$ from $A$ is (in $cm$):

$\square PQRS$ is a cyclic quadrilateral. If $m \angle P = 30^{\circ}$, then $m \angle R = \dots$ (in $^{\circ}$)

The tangents drawn from a point $P$ outside $\odot(O, 5)$ touch the circle at $A$ and $B$. If $PA = 8$,then $PB = \ldots$

If a rhombus $ABCD$ is inscribed in a circle with center $O$ and radius $r$,then the rhombus $ABCD$ is $\ldots \ldots$

In the figure,common tangents $AB$ and $CD$ to two circles intersect at $E$. Prove that $AB = CD$.