In the figure,if $PQR$ is the tangent to a circle at $Q$ whose center is $O$,$AB$ is a chord parallel to $PR$,and $\angle BQR = 70^{\circ}$,then $\angle AQB$ is equal to: (in $^{\circ}$)

$\overline{ PA }$ and $\overline{ PB }$ are the tangents to $\odot( O , r)$ drawn from a point $P$ outside a circle. If $m \angle APB = 65^{\circ}$,then $m \angle AOB = \ldots \ldots \ldots . .$ (in $^{\circ}$)

In $\Delta PQR$,$\angle Q$ is a right angle. If $PQ = 8$ and $QR = 15$,then the radius of a circle touching all the three sides of $\Delta PQR$ is $\ldots \ldots.$

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 $cm$):

Write 'True' or 'False' and give reasons for your answer.
If the angle between two tangents drawn from a point $P$ to a circle of radius $a$ and center $O$ is $90^{\circ}$,then $OP = a\sqrt{2}$.

Write 'True' or 'False' and give reasons for your answer.
$AB$ is a diameter of a circle and $AC$ is its chord such that $\angle BAC = 30^{\circ}$. If the tangent at $C$ intersects $AB$ extended at $D$,then $BC = BD$.