Derousseau's Generalization of the Malfatti circles

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

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

\(\mathbf{0a}\) \((011)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.506052104307&{}:{}&0.722905010067&{}:{}&0.783147094240&,\\B^\prime&{}\approx{}&-0.103748070570&{}:{}&0.834003087088&{}:{}&0.269744983482&,\\C^\prime&{}\approx{}&-0.122256164685&{}:{}&0.293414795243&{}:{}&0.828841369441&. \end{alignedat} \]
0a (011)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.204841683445\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}0.414992282281\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.489024658739\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.250000000000&{}:{}&0.600000000000&{}:{}&0.650000000000&. \end{alignedat} \]
0a (011)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.197085219125&{}:{}&0.602575098265&{}:{}&0.594510120861&. \end{alignedat} \]
0a (011)

Hiroyasu Kamo