Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{2a}\) \((031)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.097501286287&{}:{}&0.433199382582&{}:{}&0.469299331131&,\\B^\prime&{}\approx{}&-1.009078156460&{}:{}&-0.614525050336&{}:{}&2.623603206796&,\\C^\prime&{}\approx{}&-0.018702774091&{}:{}&0.044886657820&{}:{}&0.973816116272&. \end{alignedat} \]
2a (031)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.721998970971\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}4.036312625840\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.074811096366\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.250000000000&{}:{}&0.600000000000&{}:{}&0.650000000000&. \end{alignedat} \]
2a (031)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.050919192507&{}:{}&0.155682082933&{}:{}&0.895237109575&. \end{alignedat} \]
2a (031)

Hiroyasu Kamo