Derousseau's Generalization of the Malfatti circles

\(A=45\degree\), \(B=45\degree\), \(C=90\degree\).


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

\(\mathbf{5}\) \((202)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.851153302357&{}:{}&0.061654320878&{}:{}&0.087192376765&,\\B^\prime&{}\approx{}&0.695704992003&{}:{}&-0.679580427103&{}:{}&0.983875435101&,\\C^\prime&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&-0.000000000000&. \end{alignedat} \]
5 (202)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.210501018521\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}2.375285419106\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}1.707106781187\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.292893218813&{}:{}&0.292893218813&{}:{}&0.414213562373&. \end{alignedat} \]
5 (202)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.710677371828&{}:{}&0.028118753208&{}:{}&0.261203874964&. \end{alignedat} \]
5 (202)

Hiroyasu Kamo