Five geometric blocks with their dimensions are given below. Calculate the length of the path as shown in the image below, between points A and B.
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Once you flatten the path onto one 2D plane, check whether the horizontal distance of either endpoint from a cylinder centre exactly equals the radius of that cylinder. If it does, that tangent segment is just a straight vertical drop, and you can skip the general tangent-length formula entirely.
Step 1: Decompose the path. The belt-like path wraps the five blocks, so split it into straight segments along the block edges plus quarter-arc segments turning each corner. Step 2: Sum the parts. Add all vertical and horizontal straight lengths, then add the corner arcs (each a quarter circle of the relevant radius), giving the total length from $A$ to $B$. \[ \boxed{\text{Total} = \sum(\text{straight segments}) + \sum(\text{corner arcs})} \]
