Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{6}\) \((220)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.422649730810&{}:{}&0.211324865405&{}:{}&0.366025403784&,\\B^\prime&{}\approx{}&0.211324865405&{}:{}&0.422649730810&{}:{}&0.366025403784&,\\C^\prime&{}\approx{}&3.695074732983&{}:{}&3.695074732983&{}:{}&-6.390149465966&. \end{alignedat} \]
6 (220)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.788675134595\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.788675134595\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}13.790206641256\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.267949192431&{}:{}&0.267949192431&{}:{}&0.464101615138&. \end{alignedat} \]
6 (220)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.490353408147&{}:{}&0.490353408147&{}:{}&0.019293183706&. \end{alignedat} \]
6 (220)

Hiroyasu Kamo