MathDB

7

Part of 2007 Sharygin Geometry Olympiad

Problems(1)

tangential convex polygon, touchpoints create polygon with same angles, regular?

Source: 2007 Sharygin Geometry Olympiad Correspondence Round P7

4/25/2019
A convex polygon is circumscribed around a circle. Points of contact of its sides with the circle form a polygon with the same set of angles (the order of angles may differ). Is it true that the polygon is regular?
convex polygonInscribed circleregular polygongeometry