In the figure,if $\angle DAB = 60^{\circ}$ and $\angle ABD = 50^{\circ}$,then $\angle ACB$ is equal to: (in $^{\circ}$)

$A$ point located in the plane of a circle and which is equidistant from every point on the circle is called the ........ of the circle.

Two chords $AB$ and $AC$ of a circle subtend angles equal to $90^{\circ}$ and $150^{\circ}$,respectively,at the centre. Find $\angle BAC$,if $AB$ and $AC$ lie on the opposite sides of the centre.

$AB$ and $AC$ are two equal chords of a circle. Prove that the bisector of the angle $BAC$ passes through the centre of the circle.

In the same plane,two circles can have a maximum of ............ common chords.

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.