Derousseau's Generalization of the Malfatti circles

\(a:b:c=5:12:13\).

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[Other solutions]
[Guy]
[Lob & Richmond]

\(\mathbf{6}\) \((220)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.850871453186&{}:{}&0.071581702471&{}:{}&0.077546844343&,\\B^\prime&{}\approx{}&0.465668350749&{}:{}&-0.676406062698&{}:{}&1.210737711948&,\\C^\prime&{}\approx{}&1.234667392808&{}:{}&2.963201742740&{}:{}&-3.197869135548&. \end{alignedat} \]
6 (220)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.178954256177\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}2.794010104496\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}7.408004356849\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.166666666667&{}:{}&0.400000000000&{}:{}&0.433333333333&. \end{alignedat} \]
6 (220)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.765064993596&{}:{}&0.212307061849&{}:{}&0.022627944554&. \end{alignedat} \]
6 (220)

Hiroyasu Kamo