Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{6b}\) \((321)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&3.306997126177&{}:{}&27.683965514118&{}:{}&-29.990962640295&,\\B^\prime&{}\approx{}&-0.030101660577&{}:{}&1.108365978077&{}:{}&-0.078264317500&,\\C^\prime&{}\approx{}&-0.278649238600&{}:{}&0.668758172640&{}:{}&0.609891065960&. \end{alignedat} \]
6b (321)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-13.841982757059\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.036121992692\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-0.334379086320\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.833333333333&{}:{}&-2.000000000000&{}:{}&2.166666666667&. \end{alignedat} \]
6b (321)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.107954717346&{}:{}&1.240129193221&{}:{}&-0.132174475875&. \end{alignedat} \]
6b (321)

Hiroyasu Kamo