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Part of 1989 Bundeswettbewerb Mathematik
Problems(2)
Bundeswettbewerb Mathematik 1989 Problem 1.3
Source: Bundeswettbewerb Mathematik 1989 Round 1
9/24/2022
A convex polygon is divided into finitely many quadrilaterals. Prove that at least one of these quadrilaterals must also be convex.
polygongeometryconvex quadrilateralconvex
Bundeswettbewerb Mathematik 1989 Problem 2.3
Source: Bundeswettbewerb Mathematik 1989 Round 2
10/10/2022
Over each side of a cyclic quadrilateral erect a rectangle whose height is equal to the length of the opposite side. Prove that the centers of these rectangles form another rectangle.
geometryrectanglecyclic quadrilateralCyclic