Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{4a}\) \((211)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.672718770973&{}:{}&-0.322905010067&{}:{}&-0.349813760906&,\\B^\prime&{}\approx{}&1.353748070570&{}:{}&3.165996912912&{}:{}&-3.519744983482&,\\C^\prime&{}\approx{}&0.955589498018&{}:{}&-2.293414795243&{}:{}&2.337825297225&. \end{alignedat} \]
4a (211)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.538175016779\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-5.414992282281\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-3.822357992072\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.250000000000&{}:{}&0.600000000000&{}:{}&0.650000000000&. \end{alignedat} \]
4a (211)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.383216537776&{}:{}&-0.144771483710&{}:{}&-0.238445054066&. \end{alignedat} \]
4a (211)

Hiroyasu Kamo