Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{4c}\) \((310)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&3.814084098071&{}:{}&33.769009176847&{}:{}&-36.583093274918&,\\B^\prime&{}\approx{}&0.055524282344&{}:{}&1.088838851750&{}:{}&-0.144363134093&,\\C^\prime&{}\approx{}&0.228437733294&{}:{}&0.548250559905&{}:{}&0.223311706801&. \end{alignedat} \]
4c (310)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}11.256336392282\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.044419425875\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.182750186635\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.250000000000&{}:{}&3.000000000000&{}:{}&-3.250000000000&. \end{alignedat} \]
4c (310)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.177781512088&{}:{}&1.146089892707&{}:{}&-0.323871404795&. \end{alignedat} \]
4c (310)

Hiroyasu Kamo