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]

\(\mathbf{4b}\) \((301)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-7.470084888655&{}:{}&-9.991146350560&{}:{}&18.461231239215&,\\B^\prime&{}\approx{}&0.266247361627&{}:{}&0.241791662387&{}:{}&0.491960975985&,\\C^\prime&{}\approx{}&0.008843564140&{}:{}&-0.008843564140&{}:{}&1.000000000000&. \end{alignedat} \]
4b (301)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}18.461231239215\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.491960975985\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.016340775808\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.541196100146&{}:{}&-0.541196100146&{}:{}&1.000000000000&. \end{alignedat} \]
4b (301)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.034006143825&{}:{}&-0.020517324001&{}:{}&0.986511180176&. \end{alignedat} \]
4b (301)

Hiroyasu Kamo