Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{1c}\) \((112)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.771562266706&{}:{}&-2.741252799527&{}:{}&2.969690532821&,\\B^\prime&{}\approx{}&-0.683993829509&{}:{}&-0.094390127214&{}:{}&1.778383956722&,\\C^\prime&{}\approx{}&-2.814084098071&{}:{}&-6.753801835369&{}:{}&10.567885933440&. \end{alignedat} \]
1c (112)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.913750933176\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.547195063607\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-2.251267278456\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.250000000000&{}:{}&3.000000000000&{}:{}&-3.250000000000&. \end{alignedat} \]
1c (112)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.554506108829&{}:{}&-2.402472276392&{}:{}&3.956978385220&. \end{alignedat} \]
1c (112)

Hiroyasu Kamo