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Big regular polygons

Source: BdMO 2023 Secondary National P9

February 12, 2023
geometryorthocenterregular polygon

Problem Statement

Let A1A2…A2nA_1A_2\dots A_{2n} be a regular 2n2n-gon inscribed in circle ω\omega. Let PP be any point on the circle ω\omega. Let H1,H2,…,HnH_1,H_2,\dots, H_n be orthocenters of triangles PA1A2,PA3A4,…,PA2n−1A2nPA_1A_2, PA_3A_4,\dots, PA_{2n-1}A_{2n} respectively. Prove that H1H2…HnH_1H_2\dots H_n is a regular nn-gon.
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