Gábor Gévay,
An extension of Miquel's six-circles theorem,
Forum Geometricorum, 18 (2018) 115--118.

Abstract. We extend the classical theorem of Miquel from 6 to 2n circles (n ≥ 3). As a by-product of the proof of our theorem, we obtain the nice corollary that the product of the 2n cross ratios of the quadruples of points determining the circles is equal to 1. Moreover, the theorem can also be formulated in an equivalent form, which extends Miquel's Triangle Theorem to an arbitrary n-sided polygon.

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