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ASU 404 All Soviet Union MO 1985 pentagon contruction, symmetry wrt point

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August 5, 2019
symmetrypentagongeometric constructionmidpointsgeometry

Problem Statement

The convex pentagon ABCDEABCDE was drawn in the plane. A1A_1 was symmetric to AA with respect to BB. B1B_1 was symmetric to BB with respect to CC. C1C_1 was symmetric to CC with respect to DD. D1D_1 was symmetric to DD with respect to EE. E1E_1 was symmetric to EE with respect to AA. How is it possible to restore the initial pentagon with the compasses and ruler, knowing A1,B1,C1,D1,E1A_1,B_1,C_1,D_1,E_1 points?
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