Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{1b}\) \((103)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.958803899854&{}:{}&-0.099456183690&{}:{}&0.140652283836&,\\B^\prime&{}\approx{}&0.431277545771&{}:{}&-0.041196100146&{}:{}&0.609918554376&,\\C^\prime&{}\approx{}&1.806562964876&{}:{}&-1.806562964876&{}:{}&1.000000000000&. \end{alignedat} \]
1b (103)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.140652283836\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.609918554376\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}2.554865846209\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.707106781187&{}:{}&-0.707106781187&{}:{}&1.000000000000&. \end{alignedat} \]
1b (103)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.839961263543&{}:{}&-0.269518956564&{}:{}&0.429557693021&. \end{alignedat} \]
1b (103)

Hiroyasu Kamo