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]

\(\mathbf{4c}\) \((310)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&11.612666793933&{}:{}&17.171655583861&{}:{}&-27.784322377793&,\\B^\prime&{}\approx{}&0.227383673861&{}:{}&1.140530838933&{}:{}&-0.367914512795&,\\C^\prime&{}\approx{}&0.563522005301&{}:{}&0.563522005301&{}:{}&-0.127044010602&. \end{alignedat} \]
4c (310)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}6.558988789928\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.086852834928\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.215246252616\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&2.618033988750&{}:{}&2.618033988750&{}:{}&-4.236067977500&. \end{alignedat} \]
4c (310)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.640831647282&{}:{}&1.214008897464&{}:{}&-0.854840544746&. \end{alignedat} \]
4c (310)

Hiroyasu Kamo