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

$AB$ is a chord of a circle with centre $P$. Point $C$ is a point other than $A$ and $B$ on the major arc $AB$. If $\angle ACB = 50^{\circ}$,then find $\angle APB$. (in $^{\circ}$)

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.

If non-parallel sides of a trapezium are equal,prove that it is cyclic.

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

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.