Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{1}\) \((002)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.000000000000&{}:{}&0.366025403784&{}:{}&0.633974596216&,\\B^\prime&{}\approx{}&0.366025403784&{}:{}&-0.000000000000&{}:{}&0.633974596216&,\\C^\prime&{}\approx{}&0.036976074586&{}:{}&0.036976074586&{}:{}&0.926047850828&. \end{alignedat} \]
1 (002)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.366025403784\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}1.366025403784\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}0.137996589020\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.267949192431&{}:{}&0.267949192431&{}:{}&0.464101615138&. \end{alignedat} \]
1 (002)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.113505228594&{}:{}&0.113505228594&{}:{}&0.772989542812&. \end{alignedat} \]
1 (002)

Hiroyasu Kamo