Prove that a parallelogram circumscribing a circle is a rhombus.

In the fig. the sides of $△ABC$ inscribe a circle. $AB=7 \mathrm{cm}, BC=8 \mathrm{cm}$ and $AC=9 \mathrm{cm}$. Find the lengths of $AP, BQ$ and $CR$.

In the figure, $l$ is a line intersecting the two concentric circles whose common centre is $O$, at the points $A, B, C$ and $D$. Show that $AB=CD$.

In the figure, find $PO\text{'}$, if $PQ=12 \mathrm{cm}$ and $O\text{'}R=5 \mathrm{cm}$.

In the figure, $OD$ is perpendicular to the chord $AB$ of a circle whose centre is $O$. If $BC$ is a diameter, show that $CA=2OD$.