Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{4}\) \((200)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.984667392808&{}:{}&0.007359651452&{}:{}&0.007972955740&,\\B^\prime&{}\approx{}&0.777087866053&{}:{}&-1.797516317790&{}:{}&2.020428451737&,\\C^\prime&{}\approx{}&1.100871453186&{}:{}&2.642091487647&{}:{}&-2.742962940833&. \end{alignedat} \]
4 (200)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.018399128630\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}4.662527196317\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}6.605228719117\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.166666666667&{}:{}&0.400000000000&{}:{}&0.433333333333&. \end{alignedat} \]
4 (200)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.947852955761&{}:{}&0.024112871576&{}:{}&0.028034172663&. \end{alignedat} \]
4 (200)

Hiroyasu Kamo