Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{0b}\) \((101)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.954847509134&{}:{}&-0.541829890387&{}:{}&0.586982381253&,\\B^\prime&{}\approx{}&1.537998084118&{}:{}&-4.536793102824&{}:{}&3.998795018706&,\\C^\prime&{}\approx{}&0.373827207244&{}:{}&-0.897185297387&{}:{}&1.523358090142&. \end{alignedat} \]
0b (101)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.270914945194\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}1.845597700941\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.448592648693\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.833333333333&{}:{}&-2.000000000000&{}:{}&2.166666666667&. \end{alignedat} \]
0b (101)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.796928933401&{}:{}&-1.248724961858&{}:{}&1.451796028457&. \end{alignedat} \]
0b (101)

Hiroyasu Kamo