Derousseau's Generalization of the Malfatti circles

\(A=30\degree\), \(B=30\degree\), \(C=120\degree\).


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

\(\mathbf{0}\) \((000)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.422649730810&{}:{}&0.211324865405&{}:{}&0.366025403784&,\\B^\prime&{}\approx{}&0.211324865405&{}:{}&0.422649730810&{}:{}&0.366025403784&,\\C^\prime&{}\approx{}&0.108772844311&{}:{}&0.108772844311&{}:{}&0.782454311379&. \end{alignedat} \]
0 (000)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.788675134595\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.788675134595\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}0.405945781451\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.267949192431&{}:{}&0.267949192431&{}:{}&0.464101615138&. \end{alignedat} \]
0 (000)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.234188987528&{}:{}&0.234188987528&{}:{}&0.531622024945&. \end{alignedat} \]
0 (000)

Hiroyasu Kamo