An arc length is part of the distance around a circle. A central angle, whose vertex is at the center, tells you what fraction of the full turn the arc covers. Take that same fraction of the circumference to find the length. Comparing with a half turn instead of a full turn gives the wrong fraction.
Hints
- Hint 1
A central angle has its vertex at the circle’s center. Compare the right angle between the radii with a full turn. What fraction of the circle lies between the radii?
- Hint 2
An arc length is distance along the curved edge, not an angle in degrees. Take the angle’s fraction of the whole circumference. You don’t need to find the radius because that whole distance is already given.
Step-by-step
Take a quarter of the circumference
Step 1Find the arc’s share of the circle
No Desmos needed. The right angle gives a quarter of the circle, so the length takes one division. The radii meet at the center , making a central angle. A right angle is out of a full turn, so the shorter arc from to covers one quarter of the circle: .
- Step 2
Find the minor arc’s length
The circumference is the whole distance around the circle. Since the minor arc is one quarter of it, divide the given circumference by : . The length of minor arc is . Choice B.