Gábor Gévay,

A Remarkable Theorem on Eight Circles,
Forum Geometricorum, 18 (2018) 401--408.

Abstract. For i=1, …, 6, consider a closed chain of circles Γ_i such that every two consecutive members Γ_i and Γ_{i+1} meet in the points (A_i, B_i), with indices modulo 6. We require that both sextuples (A_1, …, A_6) and (B_1, …, B_6) are cyclic. We prove the theorem that the three lines connecting the centers of the opposite circles of the chain concur. In the rest of the paper we present a slightly more general version of this theorem.


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