Question

the circle below has a radius of 5. \\( \angle abc \\) is a central angle. the intercepted minor arc has a measure of \\( \frac { 25 } { 6 } \pi \\) units. the minor arc is what fraction of the circle? 3 of 4 questio \\( \frac { 2 } { 3 } \\) \\( \frac { 5 } { 6 } \\) \\( \frac { 5 } { 12 } \\) \\( \frac { 1 } { 6 } \\)

Explanation:

Step1: Calculate the circumference of the circle

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(r = 5\), then \(C=2\pi\times5 = 10\pi\).

Step2: Find the fraction of the arc length to the circumference

Let the arc length be \(l=\frac{25}{6}\pi\). The fraction \(f=\frac{l}{C}\). Substitute \(l\) and \(C\) into the formula: \(f=\frac{\frac{25}{6}\pi}{10\pi}\).
Simplify the expression:

$$
LATEXBLOCK0
$$

Answer:

\(\frac{5}{12}\) (the third option)