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

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.

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 $32 \text{ cm}$.

The chord which passes through the centre of the circle is called a .......... of the circle.

If two chords $AB$ and $CD$ of a circle intersect at right angles (see Fig.),prove that $\text{arc } CXA + \text{arc } DZB = \text{arc } AYD + \text{arc } BWC = \text{semicircle}$.

The region between an arc and the two radii,joining the centre to the end points of the arc is called a ........... .