Triangle Center
Level: Mathematics Education, High School, Honors Geometry, College.
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Sunday, July 27, 2014
Ajima-Malfatti Point, Tangent Circles
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The three circles seem uniquely fixed by the given triangle.
ReplyDeleteHow to construct the circles given the triangle?
Let C'' be the exsimilitude center between the tangent circles through C'
ReplyDeleteMonge-d'Alembert's theorem says that A',B' and C'' lie on line of course that point also lies on the common tangent AB.
Similarly define A'' and B''
Monge-d'Alembert's theorem also says that A'',B'' and C'' are aligned.
Triangles ABC and A'B'C' are perspective with respect to the line A''B''C''.
By Desarge's theorem, we can say that ABC and A'B'C' are perspective with respect to point P.