Distance between the Incenter and the Center of the Apollonius Circle

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Let and be the incenter and the center of the Apollonius circle of the triangle , respectively.


Let , , and be the circumradius, inradius and semiperimeter of , and .

Then [1].


Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA




[1] C. Kimberling, "Part 1: Introduction and Centers X(1)–X(1000)," Encyclopedia of Triangle Centers—ETC. (May 26, 2022) faculty.evansville.edu/ck6/encyclopedia/ETC.html.

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