In a circle with centre $O$,two chords $PQ$ and $RS$ subtend equal angles at the centre. If $PQ = 12 \text{ cm}$,then $RS = \dots \text{ cm}$.

In a circle with centre $P$,the diameter of the circle is $70 \, cm$. The chord $AB$ is at a distance of $21 \, cm$ from the centre of the circle,then $AB = \dots \, cm$.

$ABCD$ is a parallelogram. $A$ circle through $A$ and $B$ is drawn such that it intersects $AD$ at $P$ and $BC$ at $Q$. Prove that $P, Q, C,$ and $D$ are concyclic.

The line segment joining any two points on a circle is called a ........ of the circle.

$ABCD$ is a cyclic quadrilateral such that $AB$ is a diameter of the circle circumscribing it and $\angle ADC = 140^{\circ}$,then $\angle BAC$ is equal to (in $^{\circ}$)

There is one and only one circle passing through all the vertices $A, B$ and $C$ of $\Delta ABC$. This circle is called the ............. of $\Delta ABC$.