OK, so "the latter" means the arcs as it should, but then "the line segment" means its endpoints, and "it" suddenly refers back to the circle. O...kay. Then indeed it is a very elementary geometry puzzle. --Dan ----------- Mike wrote: << I think they're meant to be arcs centered on the endpoints, i.e. the point where they intersect at the top together with the endpoints of the segment form an equilateral triangle. On Sun, Oct 17, 2010 at 11:41 AM, Dan Asimov <dasimov@earthlink.net> wrote:

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

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...

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?

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_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele