TOPICS

# Johnson-Yff Circles

Since each triplet of Yff circles are congruent and pass through a single point, they obey Johnson's theorem. As a result, in each case, there is a fourth circle congruent to the original three and passing through the points of pairwise intersection. These circles have radii

 (1) (2)

and their centers are

 (3) (4)

which are Kimberling centers and , respectively.

The circle functions of the Johnson circles do not correspond to any Kimberling centers, and the Johnson-Yff circles do not pass through any Kimberling centers.

The sets of points (, , , ) and (, , , ) comprise two orthocentric systems.

Johnson Circles, Johnson's Theorem, Orthocentric System, Yff Circles

## Explore with Wolfram|Alpha

More things to try:

## References

Kimberling, C. "Encyclopedia of Triangle Centers: X(1478)=Center of Johnson-Yff Circle." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X1478.

## Referenced on Wolfram|Alpha

Johnson-Yff Circles

## Cite this as:

Weisstein, Eric W. "Johnson-Yff Circles." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Johnson-YffCircles.html