The chord ST of a circle is equal to the radius r of the circle. Find the length of arc ST
A
\(\frac{\pi r}{3}\)
B
\(\frac{\pi r}{2}\)
C
\(\frac{\pi r}{12}\)
D
\(\frac{\pi r}{6}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{ \frac{r}{2}}{r}\) Sin \(\theta\) = \(\frac{1}{2}\)
\(\theta\) = sin\(^{-1}\) (\(\frac{1}{2}\)) = 30\(^o\) = 60\(^o\)
Length of arc (minor)
ST = \(\frac{\theta}{360}\) x 2\(\pi r\)
\(\frac{60}{360} \times 2 \pi \times r = \frac{\pi}{3}\)
Source: Myschool Past Questions Archive (Record #56848)