State whether each of the following statements is true or false:
$(1)$ The region between a chord and either of its arcs is called a sector.
$(2)$ The region between an arc and the two radii,joining the centre to the end points of the arc,is called a segment.

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

The longest chord of a circle is a .......... of the circle.

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 a circle with centre $P$,$AB$ is a chord and $PA = 4\, cm$. In a circle with centre $Q$,$XY$ is a chord and $QX = 4\, cm$. If $\angle APB = 80^{\circ}$,$\angle XQY = 50^{\circ}$ and $AB = 5\, cm$,then $XY = \dots\dots\dots\, cm$.

State whether the following statements are True or False. Give reasons for your answers.
$(i)$ The line segment joining the centre to any point on the circle is a radius of the circle.
$(ii)$ $A$ circle has only a finite number of equal chords.
$(iii)$ If a circle is divided into three equal arcs,each is a major arc.
$(iv)$ $A$ chord of a circle,which is twice as long as its radius,is a diameter of the circle.
$(v)$ $A$ sector is the region between the chord and its corresponding arc.
$(vi)$ $A$ circle is a plane figure.