$A$ tangent to a circle intersects the circle in $\ldots \ldots \ldots .$

In $\Delta ABC$,$m \angle B = 90^{\circ}$. $A$ circle is inscribed in $\Delta ABC$ touching all its sides. If $AB = 16$ and $BC = 30$,find the radius of the circle.

$A$ circle touches all the sides of a quadrilateral $ABCD$. Then, the quadrilateral $ABCD$ is a:

$A$ chord $PQ$ of a circle is parallel to the tangent drawn at a point $R$ of the circle. Prove that $R$ bisects the arc $PRQ$.

Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

In the given figure,$AT$ is a tangent to the circle with center $O$ such that $OT = 4 \, cm$ and $\angle OTA = 30^{\circ}$. Then $AT$ is equal to (in $cm$):