Question

the circumference of ⊙z is 84 cm. what is the length of ⌢xy (the minor arc)?

Explanation:

Step1: Find central - angle of arc

The central - angle of arc $\overparen{XY}$ is $90^{\circ}$ since $\angle XZY = 90^{\circ}$.

Step2: Use arc - length formula

The formula for the length of an arc $s$ of a circle is $s=\frac{\theta}{360^{\circ}}\times C$, where $\theta$ is the central - angle of the arc and $C$ is the circumference of the circle. Here, $\theta = 90^{\circ}$ and $C = 84$ cm.
So, $s=\frac{90^{\circ}}{360^{\circ}}\times84$.

Step3: Calculate the arc - length

$\frac{90}{360}\times84=\frac{1}{4}\times84 = 21$ cm.

Answer:

C. 21 cm