1. **Stating the problem:** Given a circle with center O, radius AO = 21 cm, and central angle \(\angle AOB = 60^\circ\), we want to analyze the properties of segments and arcs related to this setup. 2. **Formula and rules:** - The radius of the circle is \(r = AO = 21\) cm. - The central angle \(\theta = 60^\circ\). - The length of the arc \(AB\) is given by \(s = r \times \theta\) in radians. - Convert degrees to radians: \(\theta_{rad} = \frac{\pi}{180} \times 60 = \frac{\pi}{3}\). - The chord length \(AB\) can be found using the formula \(AB = 2r \sin(\frac{\theta}{2})\). 3. **Calculate the arc length \(AB\):** $$ s = 21 \times \frac{\pi}{3} = 7\pi \approx 21.99 \text{ cm} $$ 4. **Calculate the chord length \(AB\):** $$ AB = 2 \times 21 \times \sin\left(\frac{60^\circ}{2}\right) = 42 \times \sin(30^\circ) = 42 \times 0.5 = 21 \text{ cm} $$ 5. **Interpretation:** - The radius segments AO and OB are each 21 cm. - The chord AB is 21 cm. - The arc length AB is approximately 21.99 cm. - The sector AOB corresponds to a 60° slice of the circle. **Final answers:** - Radius AO = 21 cm - Central angle \(\angle AOB = 60^\circ\) - Arc length AB \(\approx 21.99\) cm - Chord length AB = 21 cm This completes the analysis of the given problem.