Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{6}\) \((220)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.500000000000&{}:{}&0.207106781187&{}:{}&0.292893218813&,\\B^\prime&{}\approx{}&0.207106781187&{}:{}&0.500000000000&{}:{}&0.292893218813&,\\C^\prime&{}\approx{}&1.679580427103&{}:{}&1.679580427103&{}:{}&-2.359160854207&. \end{alignedat} \]
6 (220)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.707106781187\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}0.707106781187\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}5.734446273312\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.292893218813&{}:{}&0.292893218813&{}:{}&0.414213562373&. \end{alignedat} \]
6 (220)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.484716815781&{}:{}&0.484716815781&{}:{}&0.030566368437&. \end{alignedat} \]
6 (220)

Hiroyasu Kamo