Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{7}\) \((222)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.000000000000&{}:{}&0.366025403784&{}:{}&0.633974596216&,\\B^\prime&{}\approx{}&0.366025403784&{}:{}&-0.000000000000&{}:{}&0.633974596216&,\\C^\prime&{}\approx{}&3.623277963258&{}:{}&3.623277963258&{}:{}&-6.246555926517&. \end{alignedat} \]
7 (222)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.366025403784\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}1.366025403784\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}13.522257448825\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.267949192431&{}:{}&0.267949192431&{}:{}&0.464101615138&. \end{alignedat} \]
7 (222)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.472135417461&{}:{}&0.472135417461&{}:{}&0.055729165078&. \end{alignedat} \]
7 (222)

Hiroyasu Kamo