A second unusual and unintuitive solution


The trench configuration shown in the diagram consists of two disjoint trenches shown in brown. The brown circular arc actually lies on the blue circle but is shown slightly away from it in order to make the diagram more comprehensible. The straight line segments attached to the circular part are tangent to the circle at the point where the radii shown touch the circle and each has length a . The two dotted lines shown extending from these brown segments are both tangent to the circle. The remaining part of the trench extends from the dotted horizontal lines connecting the two ends of the other brown trench and the intersection of the two tangent dotted lines.