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

In the adjoining figure, $O$ is the centre of a circle and $PQ$ is a chord. If the tangent $PR$ at $P$ makes an angle of $50°$ with $PQ$, then $\angle POQ$ is

In the adjoining figure, $PA$ and $PB$ are tangents to a circle with centre $O$. If $\angle APB=50°$, then $\angle OAB$ is equal to

In the adjoining figure, sides $BC,CA$ and $AB$ of $∆ABC$ touch a circle at point $D,E$ and $F$ respectively. If $BD=4 \mathrm{cm},DC=3 \mathrm{cm}$ and $CA=8 \mathrm{cm}$, then the length of side $AB$ is

In the adjoining figure, sides $BC,CA$ and $AB$ of $∆ABC$ touch a circle at the points $PQ$ and $R$ respectively. If$PC=5 \mathrm{cm},AR=4 \mathrm{cm}$  and $RB=6 \mathrm{cm}$, then the perimeter of $∆ABC$ is

In the adjoining figure, $PA$ and $PB$ are tangents at points $A$ and $B$ respectively to a circle with centre $O$. If $C$ is a point on the circle and $\angle APB=40°$, then $\angle ACB$ is equal to

In the adjoining figure, two circles touch each other at $A. BC$ and $AP$ are common tangents to these circles. If $BP=3.8 \mathrm{cm}$, then the length of $BC$ is equal to