$\odot(O, 17)$ and $\odot(O, 15)$ are concentric circles. The chord $\overline{AB}$ of $\odot(O, 17)$ touches $\odot(O, 15)$. Then $AB = \ldots$

$AB$ is a diameter and $AC$ is a chord of a circle with centre $O$ such that $\angle BAC = 30^{\circ}$. The tangent at $C$ intersects the extended $AB$ at a point $D$. Prove that $BC = BD$.

$A$ tangent to a circle forms an angle of measure $\ldots \ldots \ldots \ldots$ with the radius drawn at the point of contact. (in $^{\circ}$)

Point $P$ lies in the exterior of $\odot(O, r)$. $\overleftrightarrow{PQ}$ touches the circle at $Q$. If $PO = 26$ and $PQ = 10$,then find the diameter of the circle.

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

$A$ tangent from $P$,a point in the exterior of a circle,touches the circle at $Q$. If $OP = 29$ and $PQ = 20$,then the diameter of the circle is: