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]

\(\mathbf{1}\) \((002)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.076120467489&{}:{}&0.324423348821&{}:{}&0.599456183690&,\\B^\prime&{}\approx{}&0.324423348821&{}:{}&0.076120467489&{}:{}&0.599456183690&,\\C^\prime&{}\approx{}&0.042301124316&{}:{}&0.042301124316&{}:{}&0.915397751368&. \end{alignedat} \]
1 (002)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.248302881333\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}1.248302881333\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}0.162764534548\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.259891532474&{}:{}&0.259891532474&{}:{}&0.480216935052&. \end{alignedat} \]
1 (002)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.126120751079&{}:{}&0.126120751079&{}:{}&0.747758497842&. \end{alignedat} \]
1 (002)

Hiroyasu Kamo