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Circles, Tangents, and Heptagon Diagonals

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Nick Halsey



Two circles are centered at intersection points of diagonals of a regular hepatgon. It turns out that circles centered at intersection points in regular polygons (particularly interestingly with polygons of odd numbers of sides) can be tangent to many other diagonals of that polygon. Try resizing the circles by dragging the green points. How many diagonals can each circle be tangent to?

Ready for more? Check out the nonagon version!

Tags: Heptagon, circles, tangents, diagonals, geometry
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