# An Original Heptagonal Problem

Geometry Level 5

Consider the above construction on a regular heptagon where the distance of the point of intersection of the indicated diagonals from the indicated edge is called $$r$$. Also, consider the scalene triangle (not shown) whose vertices are some suitably chosen three vertices of the same regular heptagon. Let its inradius be called $$R$$. What is the ratio $$R:r$$?

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