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]

\(\mathbf{7}\) \((222)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.076120467489&{}:{}&0.324423348821&{}:{}&0.599456183690&,\\B^\prime&{}\approx{}&0.324423348821&{}:{}&0.076120467489&{}:{}&0.599456183690&,\\C^\prime&{}\approx{}&6.474538827970&{}:{}&6.474538827970&{}:{}&-11.949077655939&. \end{alignedat} \]
7 (222)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.248302881333\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}1.248302881333\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}24.912465467161\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.259891532474&{}:{}&0.259891532474&{}:{}&0.480216935052&. \end{alignedat} \]
7 (222)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.486023490490&{}:{}&0.486023490490&{}:{}&0.027953019020&. \end{alignedat} \]
7 (222)

Hiroyasu Kamo