The chord length of a chord made on an arc of a circle is equal to the radius of the circle. Find the length of the arc (in units), if the radius of the circle is 21 units. (Take $\pi =\frac{22}{7}$)

Let $O$ be the center of the circle, and $P$ and $Q$ be the endpoints of the chord.
Given that the chord length $PQ$ equals the radius ($r$), the triangle $△OPQ$ formed by the center and the chord endpoints is an equilateral triangle ($OP=OQ=PQ=r$).

Therefore, the central angle $\theta$ subtended by the arc at the center is $60^{\circ }$.

The formula for the length of an arc is:

$$\text{Arc Length}=\frac{\theta }{360^{\circ }}\times 2\pi r$$

Substituting $\theta =60^{\circ }$, $r=21$, and $\pi =\frac{22}{7}$:

$$\text{Arc Length}=\frac{60^{\circ }}{360^{\circ }}\times 2\times \frac{22}{7}\times 21$$

$$\text{Arc Length}=\frac{1}{6}\times 2\times 22\times 3=\frac{132}{6}=22\text{units}$$