Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{1b}\) \((103)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.971350761400&{}:{}&-0.343790863202&{}:{}&0.372440101802&,\\B^\prime&{}\approx{}&0.415884804830&{}:{}&-0.497185297387&{}:{}&1.081300492557&,\\C^\prime&{}\approx{}&2.056997126177&{}:{}&-4.936793102824&{}:{}&3.879795976647&. \end{alignedat} \]
1b (103)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.171895431601\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.499061765796\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}2.468396551412\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.833333333333&{}:{}&-2.000000000000&{}:{}&2.166666666667&. \end{alignedat} \]
1b (103)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.853783559874&{}:{}&-0.899114392204&{}:{}&1.045330832330&. \end{alignedat} \]
1b (103)

Hiroyasu Kamo