TOPICS
Search

Stevanović Circle


The Stevanovic circle is a central circle with center X_(650), which has center function

 alpha_(650)=cosB-cosC,
(1)

It has radius

 R_S=1/2sqrt((abc(a^5-a^4b-ab^4+b^5-a^4c+a^3bc+ab^3c-b^4c+abc^3-ac^4-bc^4+c^5))/((a-b)^2(a-c)^2(b-c)^2)).
(2)

It has circle function

 l=(a^2-b^2-c^2)/(2(a-b)(b-c)),
(3)

corresponding to Kimberling center X_(905).

No Kimberling centers lie on the Stevanovic circle.

StevanovicCircle

Amazingly, the Stevanović circle (shown in black above) is orthogonal to nine other circles: the Apollonius circle (with center X_(970)), Bevan circle (with center V), circumcircle (with center O), excircles radical circle (with center X_(10)), nine-point circle (with center N), orthocentroidal circle (with center X_(381)), orthoptic circle of the Steiner inellipse (with center H), polar circle (with center H), and tangential circle (with center X_(26)).


See also

Central Circle, Orthogonal Circles

Explore with Wolfram|Alpha

References

Stevanović, M. R. "The Apollonius Circle and Related Triangle Centers." Forum Geom. 3, 187-195, 2003.

Referenced on Wolfram|Alpha

Stevanović Circle

Cite this as:

Weisstein, Eric W. "Stevanović Circle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StevanovicCircle.html

Subject classifications