1. **Problem Statement:** Find the moment about point M for the rectangle ABCD inscribed in a circle of diameter 10 cm. 2. **Given Data:** - Diameter of circle = 10 cm, so radius $r = \frac{10}{2} = 5$ cm. - Rectangle ABCD with side AB = 8 cm. - Forces and angles are indicated but not fully specified in the problem statement, so we assume the moment calculation involves the force of 8 N at 20° acting at a distance related to the rectangle. 3. **Formula for Moment:** The moment $M$ about a point is given by: $$M = F \times d \times \sin(\theta)$$ where: - $F$ is the force magnitude, - $d$ is the perpendicular distance from the point to the line of action of the force, - $\theta$ is the angle between the force and the lever arm. 4. **Calculate the lever arm $d$:** Since the rectangle is inscribed in the circle, the diagonal of the rectangle equals the diameter of the circle. Using Pythagoras theorem for rectangle ABCD: $$d = \text{diagonal} = 10 \text{ cm}$$ 5. **Calculate the moment:** Given force $F = 8$ N, angle $\theta = 20^\circ$, and lever arm $d = 10$ cm, $$M = 8 \times 10 \times \sin(20^\circ)$$ Calculate $\sin(20^\circ)$: $$\sin(20^\circ) \approx 0.3420$$ So, $$M = 8 \times 10 \times 0.3420 = 27.36 \text{ N.cm}$$ 6. **Compare with options:** The calculated moment 27.36 N.cm does not match any given options (88, 152, 58, 122 N.cm). Possibly, the force or distance values or the angle need clarification. **Final answer:** Based on the given data and assumptions, the moment about M is approximately **27.36 N.cm**. If more precise force or distance data is provided, the calculation can be adjusted accordingly.