The difficult problem in the maximum and minimum problem of Olympic mathematics in primary schools

The first type, the bridge can be very wide, just connect two villages directly, and the bridge with enough width can be built on the two bridges (left)

The second type, right? , the first river vertically translates Village A to A1 with a translation distance of river width (as long as two green lines)

Similarly, the second river vertically translates Village B to B1 with a translation distance of river width (as long as two red lines), and the intersection line connecting A1B1

with the river is the location of the bridge.