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.

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.

State whether each of the following statements is true or false:
$(1)$ $A$ line segment joining any two points of a circle is a diameter of the circle.
$(2)$ For any circle, $\text{diameter} = 2 \times \text{radius}$.
$(3)$ In a circle with radius $14 \text{ cm}$, the length of a chord can be $32 \text{ cm}$.

Fill in the blanks:
$(i)$ The centre of a circle lies in . . . . . . of the circle. (exterior/ interior)
$(ii)$ $A$ point,whose distance from the centre of a circle is greater than its radius,lies in . . . . . . of the circle. (exterior/ interior)
$(iii)$ The longest chord of a circle is a . . . . . . of the circle.
$(iv)$ An arc is a . . . . . . when its ends are the ends of a diameter.
$(v)$ Segment of a circle is the region between an arc and . . . . . . of the circle.
$(vi)$ $A$ circle divides the plane,on which it lies,in . . . . . . parts.

In the figure,$AOB$ is a diameter of the circle and $C, D, E$ are any three points on the semi-circle. Find the value of $\angle ACD + \angle BED$.

Two equal chords $AB$ and $CD$ of a circle when produced intersect at a point $P$. Prove that $PB = PD$.