MathDB

6

Part of 2020 IOM

Problems(1)

Weird geometry finale

Source: International Olympiad of Metropolises (IOM) 2020 P6

12/20/2020
In convex pentagon ABCDEABCDE points A1A_1, B1B_1, C1C_1, D1D_1, E1E_1 are intersections of pairs of diagonals (BD,CE)(BD, CE), (CE,DA)(CE, DA), (DA,EB)(DA, EB), (EB,AC)(EB, AC) and (AC,BD)(AC, BD) respectively. Prove that if four of quadrilaterals AB1A1BAB_{1}A_{1}B, BC1B1CBC_{1}B_{1}C, CD1C1DCD_{1}C_{1}D, DE1D1EDE_{1}D_{1}E and EA1E1AEA_{1}E_{1}A are cyclic then the fifth one is also cyclic.
geometryDDITtrivial