Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{2b}\) \((121)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.295152490866&{}:{}&3.541829890387&{}:{}&-3.836982381253&,\\B^\prime&{}\approx{}&-1.371331417451&{}:{}&5.936793102824&{}:{}&-3.565461685373&,\\C^\prime&{}\approx{}&-0.623827207244&{}:{}&1.497185297387&{}:{}&0.126641909858&. \end{alignedat} \]
2b (121)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-1.770914945194\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-1.645597700941\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-0.748592648693\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.833333333333&{}:{}&-2.000000000000&{}:{}&2.166666666667&. \end{alignedat} \]
2b (121)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.298378035089&{}:{}&3.427615958124&{}:{}&-2.129237923035&. \end{alignedat} \]
2b (121)

Hiroyasu Kamo