Four squares and a regular hexagon. A circle with two tangents. Show that the circle is tangent to the hexagon circumcircle. Note that the right dotted tangency point does not lie on the hexagon side.
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Solution
The upper right figure is symmetric resp. the diagonal and 15° is the well known angle that connects the top corner of the square to the top of its enclosed equilateral triangle. We then check that the dimensions match using two different expressions.
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