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 $^{\circ}$)

If $ABCD$ is a cyclic quadrilateral and $m \angle B = 60^{\circ}$,then the measure of $\angle D = \dots$ (in $^{\circ}$)

$\overline{AB}$ is a chord of $\odot(O, 10)$ such that $AB = 16$. Tangents at $A$ and $B$ to the circle intersect at $P$. Find the length of $PA$.

In the following figure,if $AB = 3$,then the perimeter of $\Delta APQ$ is...........

$A$ circle with centre $O$ touches sides $\overline{AB}$,$\overline{BC}$,$\overline{CD}$ and $\overline{DA}$ of quadrilateral $ABCD$ at points $P, Q, R$ and $S$ respectively. Prove that $m \angle AOB + m \angle COD = 180^{\circ}$ and $m \angle AOD + m \angle BOC = 180^{\circ}$.

If from an external point $B$ of a circle with centre $O$,two tangents $BC$ and $BD$ are drawn such that $\angle DBC = 120^{\circ}$,prove that $BC + BD = BO$,i.e.,$BO = 2BC$.