Derousseau's Generalization of the Malfatti circles

\(A=36\degree\), \(B=36\degree\), \(C=108\degree\).

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

\(\mathbf{1}\) \((002)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.071882550435&{}:{}&0.409422702318&{}:{}&0.662459848116&,\\B^\prime&{}\approx{}&0.409422702318&{}:{}&-0.071882550435&{}:{}&0.662459848116&,\\C^\prime&{}\approx{}&0.033040781847&{}:{}&0.033040781847&{}:{}&0.933918436306&. \end{alignedat} \]
1 (002)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.481305252753\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}1.481305252753\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}0.119542671737\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.276393202250&{}:{}&0.276393202250&{}:{}&0.447213595500&. \end{alignedat} \]
1 (002)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.103537589192&{}:{}&0.103537589192&{}:{}&0.792924821616&. \end{alignedat} \]
1 (002)

Hiroyasu Kamo