1. **Stating the problem:** We need to find the perimeter of the shaded region, which consists of an arc length plus three other segments labeled (1), (2), and (3). 2. **Formula for perimeter of a shaded circular segment:** The perimeter $P$ of a shaded circular segment is given by: $$P = \text{arc length} + \text{chord length} + \text{other boundary segments}$$ 3. **Step (1) Arc length:** The arc length of a circle segment is calculated by: $$\text{Arc length} = r \theta$$ where $r$ is the radius of the large circle and $\theta$ is the central angle in radians. 4. **Step (2) Chord length:** The chord length connecting the endpoints of the arc is: $$\text{Chord length} = 2r \sin\left(\frac{\theta}{2}\right)$$ 5. **Step (3) Radius line:** The radius line from the center to the edge forming the right triangle is: $$\text{Radius} = r$$ 6. **Conclusion:** The perimeter of the shaded region is: $$P = \text{arc length} + \text{chord length} + \text{radius} = r\theta + 2r \sin\left(\frac{\theta}{2}\right) + r$$ This includes the arc length, the chord connecting the arc endpoints, and the radius line forming the triangle.