In geometry, a set of Johnson circles comprise three circles of equal radius r sharing one common point of intersection H. In such a configuration the circles usually have a total of four intersections (points where at least two of them meet): the common point H that they all share, and for each of the three pairs of circles one more intersection point (referred here as their 2-wise intersection). If any two of the circles happen to just touch tangentially they only have H as a common point, and it will then be considered that H be their 2-wise intersection as well; if they should coincide we declare their 2-wise intersection be the point diametrically opposite H. The three 2-wise intersection points define the reference triangle of the figure.
Other articles related to "johnson circles, johnson, circle":
... The three Johnson circles can be considered the reflections of the circumcircle of the reference triangle about each of the three sides of the reference triangle ... of the circum-orthic triangle, and its circumcenter maps onto the vertices of the Johnson triangle ... The Johnson triangle and its reference triangle share the same nine-point center, the same Euler line and the same nine-point circle ...
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