## Apollonius Point

Consider the Excircles , , and of a Triangle, and the Circle internally Tangent to all three. Denote the contact point of and by , etc. Then the Lines , , and Concur in this point. It has Triangle Center Function

References

Kimberling, C. Apollonius Point.'' http://cedar.evansville.edu/~ck6/tcenters/recent/apollon.html.

Kimberling, C. Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994.

Kimberling, C.; Iwata, S.; and Hidetosi, F. Problem 1091 and Solution.'' Crux Math. 13, 128-129 and 217-218, 1987.

© 1996-9 Eric W. Weisstein
1999-05-25