Derousseau's Generalization of the Malfatti circles

\(A=36\degree\), \(B=36\degree\), \(C=108\degree\).

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[Other solutions]
[Guy]
[Lob & Richmond]

\(\mathbf{5}\) \((202)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.924076763519&{}:{}&0.029000095800&{}:{}&0.046923140681&,\\B^\prime&{}\approx{}&0.610234118204&{}:{}&-0.597613662554&{}:{}&0.987379544349&,\\C^\prime&{}\approx{}&0.883691590199&{}:{}&0.883691590199&{}:{}&-0.767383180398&. \end{alignedat} \]
5 (202)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.104923332281\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}2.207847780758\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}3.197226208912\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.276393202250&{}:{}&0.276393202250&{}:{}&0.447213595500&. \end{alignedat} \]
5 (202)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.821557928802&{}:{}&0.020609298995&{}:{}&0.157832772203&. \end{alignedat} \]
5 (202)

Hiroyasu Kamo