1. The problem asks how changing the width of a pair of compasses by 1 cm affects the radius and diameter of the circle drawn. 2. Recall the definitions: - The radius of a circle is the distance from the center to any point on the circle. - The diameter is twice the radius, i.e., $$\text{diameter} = 2 \times \text{radius}$$. 3. When you widen the compasses by 1 cm, you increase the radius by 1 cm because the radius is directly set by the compass width. 4. Therefore, the radius increases by 1 cm. 5. Since the diameter is twice the radius, increasing the radius by 1 cm increases the diameter by $$2 \times 1 = 2$$ cm. 6. So, the diameter increases by 2 cm. Final answers: a) Widening a pair of compasses by 1 cm increases the radius of the circle that is drawn by 1 cm. b) Widening a pair of compasses by 1 cm increases the diameter of the circle that is drawn by 2 cm.