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.

Read more about Johnson Circles: Properties, Proofs, Further Properties

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