Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{3}\) \((022)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.234667392808&{}:{}&0.592640348548&{}:{}&0.642027044260&,\\B^\prime&{}\approx{}&0.056245467280&{}:{}&0.797516317790&{}:{}&0.146238214929&,\\C^\prime&{}\approx{}&0.149128546814&{}:{}&0.357908512353&{}:{}&0.492962940833&. \end{alignedat} \]
3 (022)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.481600871370\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.337472803683\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}0.894771280883\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.166666666667&{}:{}&0.400000000000&{}:{}&0.433333333333&. \end{alignedat} \]
3 (022)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.021329234185&{}:{}&0.603670279334&{}:{}&0.375000486481&. \end{alignedat} \]
3 (022)

Hiroyasu Kamo