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Octagon inscribed in a conic

Source: KoMaL A. 834

November 11, 2022
geometryoctagonconic section

Problem Statement

Let A1A2…A8A_1A_2\ldots A_8 be a convex cyclic octagon, and for i=1,2…,8i=1,2\ldots,8 let Bi=AiAi+3∩Ai+1Ai+4B_i=A_iA_{i+3}\cap A_{i+1}A_{i+4} (indices are meant modulo 8). Prove that points B1,…,B8B_1,\ldots, B_8 lie on the same conic section.
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