What is the Relationship Between Arcs and Central Angles?
- Arc: An arc is a segment or a portion of the circumference of a circle.
- Central Angle: It is an angle whose vertex is at the center of the circle and whose sides intercept an arc on the circle.
Examples
Practice Questions:
- In a circle with a radius of \(5 \text{ cm}\), what is the length of the arc intercepted by a central angle of \(45^\circ\)?
- A circle has a central angle that intercepts an arc of \(20 \text{ cm}\) in length. If the circle’s radius is \(8 \text{ cm}\), what is the measure of the central angle?
- \( \frac{45}{360} \times (2\pi \times 5) \approx 3.93 \text{ cm}\)
- \( \left( \frac{20}{16\pi} \right) \times 360 \approx 143.31^\circ \)
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