Write True or False and justify your answer in each of the following: Through three collinear points a circle can be drawn.

$A, B$ and $C$ are three points on a circle. Prove that the perpendicular bisectors of $AB, BC$ and $CA$ are concurrent.

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 $AB = \dots \, cm$.

The perpendicular from the centre of a circle to a chord ........... the chord.

State whether each of the following statements is true or false:
$(1)$ The collection of all the points in a plane,which are at a fixed distance from a fixed point in the plane,is called a circle.
$(2)$ The line segment joining the centre and any point on the circle is called a radius of the circle.

In a circle with centre $P$,$AB$ is a diameter and $ABCD$ is a cyclic quadrilateral. If $\angle ADC = 150^{\circ}$,then find $\angle BAC$. (in $^{\circ}$)