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

Two tangents $PQ$ and $PR$ are drawn from an external point $P$ to a circle with centre $O$. Prove that $QORP$ is a cyclic quadrilateral.

If the measure of the angle between two radii of the circle is $48^{\circ}$,then the measure of the angle between the tangents drawn at the end points of the radii is $\ldots \ldots \ldots$ (in $^{\circ}$)

Two circles with centres $O$ and $O^{\prime}$ of radii $3\, cm$ and $4\, cm$,respectively,intersect at two points $P$ and $Q$ such that $OP$ and $O^{\prime}P$ are tangents to the two circles. Find the length of the common chord $PQ$ (in $cm$).

In the figure,if $PA$ and $PB$ are tangents to the circle with center $O$ such that $\angle APB = 50^{\circ}$,then $\angle OAB$ is equal to: (in $^{\circ}$)

$P$ is a point in the exterior of a circle having centre $O$ and radius $21$. $OP = 25$. $A$ tangent from $P$ touches the circle at $Q$. Find $PQ$.