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]

\(\mathbf{0}\) \((000)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.453848561685&{}:{}&0.208611286432&{}:{}&0.337540151884&,\\B^\prime&{}\approx{}&0.208611286432&{}:{}&0.453848561685&{}:{}&0.337540151884&,\\C^\prime&{}\approx{}&0.122846377163&{}:{}&0.122846377163&{}:{}&0.754307245674&. \end{alignedat} \]
0 (000)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.754762724747\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.754762724747\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}0.444462367970\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.276393202250&{}:{}&0.276393202250&{}:{}&0.447213595500&. \end{alignedat} \]
0 (000)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.250738053924&{}:{}&0.250738053924&{}:{}&0.498523892152&. \end{alignedat} \]
0 (000)

Hiroyasu Kamo