Sandor Nagydobai Kiss and Paul Yiu, On the Tucker circles,
Forum Geometricorum, 17 (2017) 157--175.
Abstract. Parametrizing Tucker circles by the lengths of their antiparallel sides, we find conditions for which Tucker circles are congruent, orthogonal, or tangential. In particular, we show that the Gallatly circle, which is the common pedal circle of the Brocard points, is the smallest Tucker circle, not orthogonal to any Tucker circle, and congruent Tucker circles are symmetric with respect to the line joining the Brocard points. Some orthology results are also obtained.
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