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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### Famous quotes containing the words circles and/or johnson:

“Think of the wonderful *circles* in which our whole being moves and from which we cannot escape no matter how we try. The circler *circles* in these *circles*....”

—E.T.A.W. (Ernst Theodor Amadeus Wilhelm)

“Unlike Boswell, whose Journals record a long and unrewarded search for a self, *Johnson* possessed a formidable one. His life in London—he arrived twenty-five years earlier than Boswell—turned out to be a long defense of the values of Augustan humanism against the pressures of other possibilities. In contrast to Boswell, *Johnson* possesses an identity not because he has gone in search of one, but because of his allegiance to a set of assumptions that he regards as objectively true.”

—Jeffrey Hart (b. 1930)