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From this image:

shortest path

What is the shortest path between the two endpoints, given $d$ is the distance from the left endpoint to the boundary of the circle, and $r$ is the radius of the circle?

I am tied between the main diagonal and along the line, but some intermediate might work too.

JMP
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    See here: http://math.stackexchange.com/questions/227469/what-would-be-the-shortest-path-between-2-points-when-there-are-objects-obstruct – Jack Frost Nov 01 '15 at 06:21

1 Answers1

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HINT

The upper figure below depicts your arrangement with a piece of red thread fixed to the left side of the horizontal rod. We pull the thread upward as shown. The thread will take the shortest path when tight.

enter image description here

So the solution is to construct the two tangent lines to the circle from the left and from the right.

zoli
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