1. **State the problem:** We have three circles A, B, and C with diameters 10, 30, and 10 units respectively. Given that $AZ = CW$ and $YW = 3$, we need to find the lengths of segments $AZ$, $XB$, and $AC$. 2. **Identify known values:** - Diameter of circle A: 10 units, so radius $r_A = \frac{10}{2} = 5$ - Diameter of circle B: 30 units, so radius $r_B = \frac{30}{2} = 15$ - Diameter of circle C: 10 units, so radius $r_C = \frac{10}{2} = 5$ - $YW = 3$ - $AZ = CW$ 3. **Analyze the geometry:** Since $AZ = CW$ and circles A and C have the same radius, the segments $AZ$ and $CW$ are equal chords or segments related to these circles. 4. **Find $AZ$ and $CW$:** Given $YW = 3$, and assuming $YW$ is a segment between points on circles B and C, and $AZ = CW$, we can infer that $AZ = CW = YW = 3$ units. 5. **Find $XB$:** Assuming $X$ and $B$ are points on circle B, and $XB$ is a radius or segment related to circle B, the length $XB$ equals the radius of circle B, which is 15 units. 6. **Find $AC$:** $AC$ is the distance between centers of circles A and C. Since both have radius 5 and are positioned such that $AZ = CW = 3$, and considering the geometry of overlapping circles, the distance $AC$ equals the sum of their radii minus the overlap. Since $AZ = CW = 3$, the overlap is 3 units, so: $$AC = r_A + r_C - AZ = 5 + 5 - 3 = 7$$ **Final answers:** - $AZ = 3$ - $XB = 15$ - $AC = 7$