1. **Problem 1: Find the indicated measures in the circles.** 2. **Arc length of PQ:** - Given: Angle measure at R is $75^\circ$, segment QR length is 9 yd (though QR is a chord, we use the angle to find arc length). - Formula for arc length: $$\text{Arc length} = \frac{\theta}{360^\circ} \times 2\pi r$$ - We need radius $r$. Since QR is a chord, and no radius given, assume radius $r=9$ yd (approximation for this problem). - Calculate arc length: $$\text{Arc length} = \frac{75}{360} \times 2\pi \times 9 = \frac{75}{360} \times 18\pi = \frac{5}{24} \times 18\pi = \frac{90\pi}{24} = \frac{15\pi}{4} \approx 11.78 \text{ yd}$$ 3. **Circumference of ON:** - Given: Central angle $270^\circ$, circumference $61.26$ m. - Since circumference is total circle length, $C = 61.26$ m. 4. **Radius of OG:** - Given: Central angle $150^\circ$, radius $EG = 10.5$ ft. - Radius $r = 10.5$ ft. --- 5. **Problem 2: Tire travel distance for 25 revolutions.** - Tire circumference $C = 2\pi r$. - Radius $r$ is half the diameter; assume diameter $d$ given or use tire dimension (not specified, so assume radius $r$). - Distance traveled = number of revolutions $\times$ circumference. Since tire dimensions are not specified, assume radius $r$ is given or use a placeholder. If radius $r$ is known, then: $$\text{Distance} = 25 \times 2\pi r = 50\pi r$$ Without radius, cannot compute exact distance. --- **Final answers:** - Arc length of PQ $\approx 11.78$ yd - Circumference of ON $= 61.26$ m - Radius of OG $= 10.5$ ft - Tire travel distance $= 50\pi r$ ft (depends on tire radius)