Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{4b}\) \((301)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-1.056997126177&{}:{}&-24.683965514118&{}:{}&26.740962640295&,\\B^\prime&{}\approx{}&0.196768327244&{}:{}&0.291634021923&{}:{}&0.511597650834&,\\C^\prime&{}\approx{}&0.028649238600&{}:{}&-0.068758172640&{}:{}&1.040108934040&. \end{alignedat} \]
4b (301)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}12.341982757059\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.236121992692\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.034379086320\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.833333333333&{}:{}&-2.000000000000&{}:{}&2.166666666667&. \end{alignedat} \]
4b (301)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.099493101869&{}:{}&-0.155897865706&{}:{}&1.056404763837&. \end{alignedat} \]
4b (301)

Hiroyasu Kamo