Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{3a}\) \((033)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.147963892575&{}:{}&0.408977331564&{}:{}&0.443058775861&,\\B^\prime&{}\approx{}&-0.183384247027&{}:{}&0.706585204757&{}:{}&0.476799042270&,\\C^\prime&{}\approx{}&-0.069165380380&{}:{}&0.165996912912&{}:{}&0.903168467468&. \end{alignedat} \]
3a (033)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.681628885940\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}0.733536988108\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.276661521521\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.250000000000&{}:{}&0.600000000000&{}:{}&0.650000000000&. \end{alignedat} \]
3a (033)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.036689010756&{}:{}&0.391640212356&{}:{}&0.645048798400&. \end{alignedat} \]
3a (033)

Hiroyasu Kamo