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]

\(\mathbf{4}\) \((200)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.979579673804&{}:{}&0.007799870546&{}:{}&0.012620455651&,\\B^\prime&{}\approx{}&0.589033892950&{}:{}&-0.542110752268&{}:{}&0.953076859319&,\\C^\prime&{}\approx{}&1.734342398551&{}:{}&1.734342398551&{}:{}&-2.468684797102&. \end{alignedat} \]
4 (200)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.028220196742\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}2.131144645218\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}6.274909746087\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.276393202250&{}:{}&0.276393202250&{}:{}&0.447213595500&. \end{alignedat} \]
4 (200)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.930265846940&{}:{}&0.023336305710&{}:{}&0.046397847350&. \end{alignedat} \]
4 (200)

Hiroyasu Kamo