The figure shows circles A (radius r)
and B (radius r) tangent at C. A common tangent line is tangent
to the circles at C and D, respectively. Points F and G are on
DE, M is on arc CD and H is on arc CE. If FGHM is a square of
side x, prove that .
References: Fukagawa Hidetoshi, Tony Rothman, "Sacred
Mathematics: Japanese Temple Geometry" (Princenton
University Press, 2008).