Euclid's Muse

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Circles, Tangents and Nonagon Diagonals

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Nick Halsey



You may want to see the heptagon version before attempting this one

Every diagonal within a regular nonagon is drawn. Circles are centered at each intersection of diagonals along a vertical axis (these same constructions can be made nine times around the nonagon). Each circle can be tangent to at least 4 diagonals when the circle is at least 2 different sizes. Unnecessary diagonals have been hidden. Drag the green points to resize the circles. Can you find all 13 positions where a circle is tangent to at least 4 diagonals?

Hint: sometimes the circle is not entirely contained within the nonagon.

Ready for more? Check out the hendecagon version!

Tags: Nonagons, Circles, Diagonals, Tangents, Puzzler
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