Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{2c}\) \((130)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.037016188229&{}:{}&0.444194258749&{}:{}&-0.481210446978&,\\B^\prime&{}\approx{}&4.221126147106&{}:{}&7.753801835369&{}:{}&-10.974927982475&,\\C^\prime&{}\approx{}&0.455995886339&{}:{}&1.094390127214&{}:{}&-0.550386013553&. \end{alignedat} \]
2c (130)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.148064752916\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}3.376900917685\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.364796709071\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.250000000000&{}:{}&3.000000000000&{}:{}&-3.250000000000&. \end{alignedat} \]
2c (130)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.983662115547&{}:{}&1.220685668015&{}:{}&-1.204347783562&. \end{alignedat} \]
2c (130)

Hiroyasu Kamo