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equal polygons with vertices of one interior or on border of other, coincide?

Source: 2012 Oral Moscow Geometry Olympiad grades 8-9 p2

September 8, 2019
congruentpolygoninteriorgeometry

Problem Statement

Two equal polygons FF and FF' are given on the plane. It is known that the vertices of the polygon FF belong to FF' (may lie inside it or on the border). Is it true that all the vertices of these polygons coincide?