$\overline{PA}$ is a tangent to $\odot(O, r)$ drawn from a point $P$ outside a circle. If $m\angle AOP = 40^\circ$,then $m\angle OPA = \ldots$ (in $^\circ$)

$A$ tangent to a circle is perpendicular to ..... drawn from the point of contact.

In the figure,tangents $PQ$ and $PR$ are drawn to a circle such that $\angle RPQ = 30^{\circ}$. $A$ chord $RS$ is drawn parallel to the tangent $PQ$. Find the $\angle RQS$. (in $^{\circ}$)

$A$ line drawn from the centre $O$ of a circle with radius $7 \, cm$ intersects the tangent at point $P$ on the circle at point $Q$,such that $PQ = 24 \, cm$. Find $OQ$.

In the following figure,if $AB = 15$,then $CD = \ldots$

Two concentric circles having radii $5$ and $13$ are given. The chord of the circle with larger radius touches the circle with smaller radius. Then the length of the chord is $\ldots \ldots \ldots \ldots.$