Derousseau's Generalization of the Malfatti circles

\(A=22.5\degree\), \(B=22.5\degree\), \(C=135\degree\).

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

\(\mathbf{4}\) \((200)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.990074754576&{}:{}&0.003485282707&{}:{}&0.006439962716&,\\B^\prime&{}\approx{}&0.533451499915&{}:{}&-0.519141344633&{}:{}&0.985689844718&,\\C^\prime&{}\approx{}&3.937549278574&{}:{}&3.937549278574&{}:{}&-6.875098557148&. \end{alignedat} \]
4 (200)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.013410528131\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}2.052592844548\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}15.150740930607\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.259891532474&{}:{}&0.259891532474&{}:{}&0.480216935052&. \end{alignedat} \]
4 (200)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.965830569058&{}:{}&0.009369094039&{}:{}&0.024800336903&. \end{alignedat} \]
4 (200)

Hiroyasu Kamo