# Johnson Circles

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 CirclesProperties, Proofs, Further Properties

### Other articles related to "johnson circles, johnson, circle":

Johnson Circles - Further Properties
... 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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