Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{5c}\) \((312)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-1.980750764737&{}:{}&-35.769009176847&{}:{}&38.749759941585&,\\B^\prime&{}\approx{}&-0.305524282344&{}:{}&0.511161148250&{}:{}&0.794363134093&,\\C^\prime&{}\approx{}&-0.061771066627&{}:{}&-0.148250559905&{}:{}&1.210021626533&. \end{alignedat} \]
5c (312)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-11.923003058949\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.244419425875\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-0.049416853302\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.250000000000&{}:{}&3.000000000000&{}:{}&-3.250000000000&. \end{alignedat} \]
5c (312)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.204286721104&{}:{}&-0.253511717770&{}:{}&1.457798438875&. \end{alignedat} \]
5c (312)

Hiroyasu Kamo