Construction of the Apollonius Point. See http://faculty.evansville.edu/ck6/tcenters/recent/apollon.html
for the definition, and http://whistleralley.com/tangents/tangents.htm and
http://whistleralley.com/inversion/inversion.htm for the methods of construction.
The triangle is defined by free points A, B, and C. Construction of the three excircles
Ea, Eb, and Ec was pretty simple given the angle-bisection tool. Construction of the
circle E tangent to Ea, Eb, and Ec and encompassing them was not so simple.
Cinderella's tool for inversions (mirroring defined by a circle) was invaluable in this
complicated construction. No CindyScript was used.
This construction: Just for fun. (To see how it was done, download the construction.
Use the bookmarklet you can find at the Cinderella Support Forum, topic
"Learning from blog posts".)
For more information on different triangle centers, see
http://faculty.evansville.edu/ck6/tcenters/index.html.
-- David Bakin
