Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{0}\) \((000)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.301497473876&{}:{}&0.335281212540&{}:{}&0.363221313584&,\\B^\prime&{}\approx{}&0.099419031209&{}:{}&0.642091487647&{}:{}&0.258489481144&,\\C^\prime&{}\approx{}&0.084368200921&{}:{}&0.202483682210&{}:{}&0.713148116870&. \end{alignedat} \]
0 (000)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.838203031349\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.596514187255\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}0.506209205524\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.166666666667&{}:{}&0.400000000000&{}:{}&0.433333333333&. \end{alignedat} \]
0 (000)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.151261011934&{}:{}&0.392458182810&{}:{}&0.456280805256&. \end{alignedat} \]
0 (000)

Hiroyasu Kamo