Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{5b}\) \((303)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.626172792756&{}:{}&-4.485926486933&{}:{}&4.859753694177&,\\B^\prime&{}\approx{}&0.185766159067&{}:{}&0.331241827360&{}:{}&0.482992013574&,\\C^\prime&{}\approx{}&0.045152490866&{}:{}&-0.108365978077&{}:{}&1.063213487212&. \end{alignedat} \]
5b (303)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}2.242963243466\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.222919390880\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.054182989039\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.833333333333&{}:{}&-2.000000000000&{}:{}&2.166666666667&. \end{alignedat} \]
5b (303)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.141184169980&{}:{}&-0.148680210238&{}:{}&1.007496040259&. \end{alignedat} \]
5b (303)

Hiroyasu Kamo