Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{0c}\) \((110)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.207106781187&{}:{}&0.500000000000&{}:{}&-0.707106781187&,\\B^\prime&{}\approx{}&0.500000000000&{}:{}&1.207106781187&{}:{}&-0.707106781187&,\\C^\prime&{}\approx{}&4.054865846209&{}:{}&4.054865846209&{}:{}&-7.109731692418&. \end{alignedat} \]
0c (110)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.292893218813\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.292893218813\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}2.375285419106\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.707106781187&{}:{}&1.707106781187&{}:{}&-2.414213562373&. \end{alignedat} \]
0c (110)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.170209910570&{}:{}&1.170209910570&{}:{}&-1.340419821139&. \end{alignedat} \]
0c (110)

Hiroyasu Kamo