Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{3}\) \((022)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.561722341219&{}:{}&0.571630050544&{}:{}&0.990092290675&,\\B^\prime&{}\approx{}&0.016827217576&{}:{}&0.954027186633&{}:{}&0.029145595791&,\\C^\prime&{}\approx{}&1.366025403784&{}:{}&1.366025403784&{}:{}&-1.732050807569&. \end{alignedat} \]
3 (022)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}2.133352391763\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.062800030943\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}5.098076211353\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.267949192431&{}:{}&0.267949192431&{}:{}&0.464101615138&. \end{alignedat} \]
3 (022)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.015265859359&{}:{}&0.880771091600&{}:{}&0.103963049041&. \end{alignedat} \]
3 (022)

Hiroyasu Kamo