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]

\(\mathbf{0c}\) \((110)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.396802246667&{}:{}&0.642039521920&{}:{}&-1.038841768588&,\\B^\prime&{}\approx{}&0.642039521920&{}:{}&1.396802246667&{}:{}&-1.038841768588&,\\C^\prime&{}\approx{}&7.955791036595&{}:{}&7.955791036595&{}:{}&-14.911582073190&. \end{alignedat} \]
0c (110)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.245237275253\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.245237275253\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}3.038841768588\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&2.618033988750&{}:{}&2.618033988750&{}:{}&-4.236067977500&. \end{alignedat} \]
0c (110)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.501399931367&{}:{}&1.501399931367&{}:{}&-2.002799862733&. \end{alignedat} \]
0c (110)

Hiroyasu Kamo