Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{3c}\) \((132)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.796317145104&{}:{}&-2.444194258749&{}:{}&2.647877113645&,\\B^\prime&{}\approx{}&-4.471126147106&{}:{}&-6.153801835369&{}:{}&11.624927982475&,\\C^\prime&{}\approx{}&-0.289329219672&{}:{}&-0.694390127214&{}:{}&1.983719346886&. \end{alignedat} \]
3c (132)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.814731419583\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-3.576900917685\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-0.231463375738\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.250000000000&{}:{}&3.000000000000&{}:{}&-3.250000000000&. \end{alignedat} \]
3c (132)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.315333151301&{}:{}&-2.032833073008&{}:{}&3.348166224310&. \end{alignedat} \]
3c (132)

Hiroyasu Kamo