In a circle with radius $13 \, cm$,find the length of a chord lying at a distance of $12 \, cm$ from the centre. (in $, cm$)

Write True or False and justify your answer in each of the following:
Two congruent circles with centres $O$ and $O^{\prime}$ intersect at two points $A$ and $B$. Then $\angle AOB = \angle AO^{\prime}B$.

In a circle with radius $17 \, cm$,the length of a chord is $30 \, cm$. Find the distance of the chord from the centre. (in $, cm$)

If $AB = 12 \, cm$,$BC = 16 \, cm$ and $AB$ is perpendicular to $BC$,then the radius of the circle passing through the points $A, B$ and $C$ is (in $cm$)

The line segment joining the centre and any point on the circle is called a .......... of the circle.

Two circles with centres $O$ and $O'$ intersect at two points $A$ and $B$. $A$ line $PQ$ is drawn parallel to $OO'$ through $A$ (or $B$) intersecting the circles at $P$ and $Q$. Prove that $PQ = 2 OO'$.