State whether each of the following statements is true or false:
$(1)$ $A$ piece of a circle between two points on a circle is called an arc of the circle.
$(2)$ The length of the complete circle is called its circumference.

In the given figure,if $\angle BCD = 40^{\circ}$ and $\angle BAE = 65^{\circ},$ then find the values of $a, b,$ $c$ and $d$.

The length of the complete circle is called its ............

State whether each of the following statements is true or false:
$(1)$ For any two points on a circle,the line segment joining them is called a chord of the circle.
$(2)$ The length of a diameter of a circle is half the length of its radius.

In a circle with centre $P$,$AB$ is a chord and point $C$ is a point other than $A$ and $B$ on the major arc $AB$. If $\angle ACB = 47^{\circ},$ then $\angle APB = $ .......... (in $^{\circ}$)

In a cyclic quadrilateral $ABCD$,diagonals $AC$ and $BD$ intersect at $P$. If $\angle BAC = 52^{\circ}$ and $\angle ADB = 78^{\circ}$,then find $\angle ABC$. (in $^{\circ}$)