Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{2}\) \((020)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.165631799079&{}:{}&0.559503263558&{}:{}&0.606128535521&,\\B^\prime&{}\approx{}&0.010221738128&{}:{}&0.963201742740&{}:{}&0.026576519133&,\\C^\prime&{}\approx{}&0.551497473876&{}:{}&1.323593937302&{}:{}&-0.875091411178&. \end{alignedat} \]
2 (020)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.398758158895\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.061330428767\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}3.308984843256\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.166666666667&{}:{}&0.400000000000&{}:{}&0.433333333333&. \end{alignedat} \]
2 (020)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.030941555648&{}:{}&0.875722840244&{}:{}&0.093335604108&. \end{alignedat} \]
2 (020)

Hiroyasu Kamo