Problem #461

Shortest Road
Public 12/29/17 7xp Math 55.6%

A river forming a bend has the following shape:
- bank b1 passes at points (0,0) and (9,9)
- bank b2 passes at point (0,2) and is parallel to b1
- bank b4 passes at points (0,13) and (9,9)
- bank b3 passes at point (0,12) and is parallel to b4


We want to build a road between points A (2,15) and B (7,2)
The constraint is that bridges over the river must be perpendicular to the banks.
What is the shortest possible distance (A,B) ?

Give your answer rounded to 10 digits after the decimal point.



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