If $ABCD$ is a cyclic quadrilateral and $m \angle B = 60^{\circ}$,then the measure of $\angle D = \dots$ (in $^{\circ}$)

In $\Delta ABC$,$m \angle B = 90^{\circ}$. $A$ circle touches all the sides of $\Delta ABC$. If $AB + AC = 32$ and $BC = 24$,then find the radius of the incircle.

If from an external point $B$ of a circle with centre $O$,two tangents $BC$ and $BD$ are drawn such that $\angle DBC = 120^{\circ}$,prove that $BC + BD = BO$,i.e.,$BO = 2BC$.

$A$ tangent $\stackrel{\leftrightarrow}{AB}$ of $\odot(P, r)$ touches the circle at $Q$. If a perpendicular is drawn from $P$ onto $AB$,then the foot of the perpendicular is ....

If $\odot(P, r)$ touches all the sides of a quadrilateral $ABCD$,then $ABCD$ is a $\ldots \ldots \ldots \ldots$

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