Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{0c}\) \((110)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.061771066627&{}:{}&0.741252799527&{}:{}&-0.803023866155&,\\B^\prime&{}\approx{}&0.433993829509&{}:{}&1.694390127214&{}:{}&-1.128383956722&,\\C^\prime&{}\approx{}&2.980750764737&{}:{}&7.153801835369&{}:{}&-9.134552600107&. \end{alignedat} \]
0c (110)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.247084266509\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.347195063607\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}2.384600611790\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.250000000000&{}:{}&3.000000000000&{}:{}&-3.250000000000&. \end{alignedat} \]
0c (110)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.975882762576&{}:{}&1.801920325713&{}:{}&-1.777803088289&. \end{alignedat} \]
0c (110)

Hiroyasu Kamo