Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{3a}\) \((033)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.251697118667&{}:{}&0.309957202211&{}:{}&0.438345679122&,\\B^\prime&{}\approx{}&-0.806562964876&{}:{}&0.665910681040&{}:{}&1.140652283836&,\\C^\prime&{}\approx{}&-0.099456183690&{}:{}&0.099456183690&{}:{}&1.000000000000&. \end{alignedat} \]
3a (033)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.438345679122\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}1.140652283836\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.140652283836\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.707106781187&{}:{}&0.707106781187&{}:{}&1.000000000000&. \end{alignedat} \]
3a (033)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.087674443642&{}:{}&0.273239171748&{}:{}&0.814435271894&. \end{alignedat} \]
3a (033)

Hiroyasu Kamo