Go Geometry Problem Geometry Problem 336: Proving a Conclusion about a Square Inscribed in Tangent Circles with a Common Tangent Line

The figure shows circles A (radius r) and B (radius r) tangent at point C. A common tangent line is tangent to the circles at points D and E, respectively. Points F and G are on line segment DE, point M is on arc CD, and point H is on arc CE. If FGHM is a square of side length x, prove the following conclusion Conclusion to prove.


Tangent circles and square

References: Fukagawa Hidetoshi, Tony Rothman, "Sacred Mathematics: Japanese Temple Geometry" (Princenton University Press, 2008).


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