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Found problems: 1

2006 Tournament of Towns, 1
Two regular polygons, a $7$-gon and a $17$-gon are given. For each of them two circles are drawn, an inscribed circle and a circumscribed circle. It happened that rings containing the polygons have equal areas. Prove that sides of the polygons are equal. (3)
area heptagon circumcircle geometry 17-gon incircle regular polygon regular polygons