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]

\(\mathbf{2c}\) \((130)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.140530838933&{}:{}&0.227383673861&{}:{}&-0.367914512795&,\\B^\prime&{}\approx{}&17.171655583861&{}:{}&11.612666793933&{}:{}&-27.784322377793&,\\C^\prime&{}\approx{}&0.563522005301&{}:{}&0.563522005301&{}:{}&-0.127044010602&. \end{alignedat} \]
2c (130)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.086852834928\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}6.558988789928\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.215246252616\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&2.618033988750&{}:{}&2.618033988750&{}:{}&-4.236067977500&. \end{alignedat} \]
2c (130)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.214008897464&{}:{}&0.640831647282&{}:{}&-0.854840544746&. \end{alignedat} \]
2c (130)

Hiroyasu Kamo