Question

What is the difference between chord length and arc length?

Answer 1

Hint: Chord means the line segment joining two points on a circle and arc means the portion of the circle between two points on the circle. So, the difference between chord length and arc length is that chord length gives us the length between two points and an arc length gives us the total portion covered between two points.

Complete step-by-step answer:
Both chord length and arc length are terms used for circles. Let us first see the definition of circle.
A set of all points in a plane equidistant from a fixed point called center is known as a circle. The distance between the center and each point in the plane that forms a circle is known as the radius.
The line segment connecting two points on this circle is known as chord and the distance between these two points is known as the chord length.
If the chord passes through the center of the circle, then it is known as the diameter of the circle. The diameter of the circle is twice the radius of the circle.
$ \Rightarrow D = 2R$
A central angle is an angle whose vertex coincides with the center of the circle. The relation between central angle and the chord length is given by
 $ \Rightarrow a = 2R\sin \dfrac{\alpha }{2}$.
The portion of the circle between two given points is known as the arc of the circle. The length of this arc is given by the central angle subtended by this arc. The formula for the length of arc is given by
$ \Rightarrow s = \alpha R$.

Note: As the chord length is the distance between two points, it is measured in cm or m and as the arc length is the portion of the circle covered, it is measured in radian$\left( \pi \right)$.