In a circle with centre $P$,$AB$ and $CD$ are equal chords. If $\angle APB = 80^{\circ},$ then $\angle CPD =$ .......... (in $^{\circ}$)

$AB$ 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 $\angle ACB + \angle APB = 135^{\circ}$,then find $\angle ACB$ and $\angle APB$.

In a circle with centre $P$,$AB$ and $CD$ are equal chords. If $\angle APB = 80^{\circ}$,then find $\angle CPD$. (in $^{\circ}$)

$ABCD$ 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 $^{\circ}$)

State whether each of the following statements is true or false:
$(1)$ $A$ circle divides the plane on which it lies into three parts.
$(2)$ $A$ point,whose distance from the centre of a circle is greater than its radius,lies in the interior of the circle.

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