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]

\(\mathbf{6}\) \((220)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.453848561685&{}:{}&0.208611286432&{}:{}&0.337540151884&,\\B^\prime&{}\approx{}&0.208611286432&{}:{}&0.453848561685&{}:{}&0.337540151884&,\\C^\prime&{}\approx{}&2.584993206903&{}:{}&2.584993206903&{}:{}&-4.169986413806&. \end{alignedat} \]
6 (220)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.754762724747\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.754762724747\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}9.352593283263\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.276393202250&{}:{}&0.276393202250&{}:{}&0.447213595500&. \end{alignedat} \]
6 (220)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.487834409624&{}:{}&0.487834409624&{}:{}&0.024331180752&. \end{alignedat} \]
6 (220)

Hiroyasu Kamo