Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{7c}\) \((332)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.544004113661&{}:{}&-5.471950636069&{}:{}&5.927946522408&,\\B^\prime&{}\approx{}&-0.342656599941&{}:{}&0.451749440095&{}:{}&0.890907159846&,\\C^\prime&{}\approx{}&-0.037016188229&{}:{}&-0.088838851750&{}:{}&1.125855039979&. \end{alignedat} \]
7c (332)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-1.823983545356\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.274125279953\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-0.029612950583\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.250000000000&{}:{}&3.000000000000&{}:{}&-3.250000000000&. \end{alignedat} \]
7c (332)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.128676649241&{}:{}&-0.237595209797&{}:{}&1.366271859037&. \end{alignedat} \]
7c (332)

Hiroyasu Kamo