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Pentabuild
Age 16 to 18
Challenge Level 
The angles are all multiples of $36^o$ and the figure has many
symmetries. Form a quadratic equation by equating ratios of
corresponding sides in the similar triangles.
In explaining the construction look for $\sqrt 5$ appearing from triangle $YOS$ and the golden ratio appearing as the radius of circle $C_5$ (see Note). Concentrate on cosines which, in this case, are easier than the sines to find exactly.
In explaining the construction look for $\sqrt 5$ appearing from triangle $YOS$ and the golden ratio appearing as the radius of circle $C_5$ (see Note). Concentrate on cosines which, in this case, are easier than the sines to find exactly.
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