The wording seems to have gone awry: << a small circle surrounded by a pair of larger arcs tangent to it, the latter centred on a line segment also tangent to it
since "the latter" must refer to the circle, which is the former, not the latter. Assuming this is what's intended: Seems to me the inner circle C can have any radius r, and there will always be a corresponding picture satisfying the stated conditions. Then as long as the two arcs (convex outward) ending at the segment's endpoints have a (common) radius R > max{1,r}, they can be swung around from outside C until becoming tangent to it -- and then extended to meet at the perpendicular bisector of the segment. So there appear to be two degrees of freedom here. --Dan ----------- Fred wrote: << Chris Maslanka (Guardian newspaper, Saturday October 16th 2010) diagrams the following bilaterally symmetric architectural decoration, comprising a small circle surrounded by a pair of larger arcs tangent to it, the latter centred on a line segment also tangent to it; and asks, given the segment has unit length, what radius has the circle? @ @ @ @ * * @ @ * * @ @ * * @ @ * * @ @ * * @ @ * * @ @ * * @ @----------*-*----------@
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele