Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{1a}\) \((013)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.041196100146&{}:{}&0.431277545771&{}:{}&0.609918554376&,\\B^\prime&{}\approx{}&-0.099456183690&{}:{}&0.958803899854&{}:{}&0.140652283836&,\\C^\prime&{}\approx{}&-1.806562964876&{}:{}&1.806562964876&{}:{}&1.000000000000&. \end{alignedat} \]
1a (013)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.609918554376\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}0.140652283836\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}2.554865846209\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.707106781187&{}:{}&0.707106781187&{}:{}&1.000000000000&. \end{alignedat} \]
1a (013)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.269518956564&{}:{}&0.839961263543&{}:{}&0.429557693021&. \end{alignedat} \]
1a (013)

Hiroyasu Kamo