Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{2}\) \((020)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.531377455822&{}:{}&0.560523051614&{}:{}&0.970854404209&,\\B^\prime&{}\approx{}&0.005720218646&{}:{}&0.984372072030&{}:{}&0.009907709325&,\\C^\prime&{}\approx{}&2.366025403784&{}:{}&2.366025403784&{}:{}&-3.732050807569&. \end{alignedat} \]
2 (020)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}2.091900507436\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.021348146616\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}8.830127018922\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.267949192431&{}:{}&0.267949192431&{}:{}&0.464101615138&. \end{alignedat} \]
2 (020)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.016402709845&{}:{}&0.946362226653&{}:{}&0.037235063502&. \end{alignedat} \]
2 (020)

Hiroyasu Kamo