Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{6c}\) \((330)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.289329219672&{}:{}&3.471950636069&{}:{}&-3.761279855741&,\\B^\prime&{}\approx{}&0.092656599941&{}:{}&1.148250559905&{}:{}&-0.240907159846&,\\C^\prime&{}\approx{}&0.203682854896&{}:{}&0.488838851750&{}:{}&0.307478293354&. \end{alignedat} \]
6c (330)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.157316878690\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.074125279953\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.162946283917\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.250000000000&{}:{}&3.000000000000&{}:{}&-3.250000000000&. \end{alignedat} \]
6c (330)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.243410668045&{}:{}&1.054609448743&{}:{}&-0.298020116789&. \end{alignedat} \]
6c (330)

Hiroyasu Kamo