The maximum area of a triangle inscribed in a semicircle with diameter $50 \, cm$ is ........... $cm^{2}$.

In $Fig.$,$PQ$ is a chord of a circle and $PT$ is the tangent at $P$ such that $\angle QPT = 60^{\circ}$. Then $\angle PRQ$ is equal to (in $^{\circ}$)

In the following figure,find the radius of the circle.

Write 'True' or 'False' and give reasons for your answer.
If a number of circles pass through the end points $P$ and $Q$ of a line segment $PQ$,then their centres lie on the perpendicular bisector of $PQ$.

From a point $P$ which is at a distance of $13 \, cm$ from the centre $O$ of a circle of radius $5 \, cm$,the pair of tangents $PQ$ and $PR$ to the circle are drawn. Then the area of the quadrilateral $PQOR$ is (in $cm^2$)

$\overline{AB}$ is a chord of $\odot(O, 13)$ such that $AB = 24$. Tangents at $A$ and $B$ to the circle intersect at $P$. Find $PA$.