Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{6a}\) \((231)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.099456183690&{}:{}&-0.041196100146&{}:{}&-0.058260083544&,\\B^\prime&{}\approx{}&6.068535592272&{}:{}&3.513669746063&{}:{}&-8.582205338335&,\\C^\prime&{}\approx{}&0.748302881333&{}:{}&-0.748302881333&{}:{}&1.000000000000&. \end{alignedat} \]
6a (231)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.058260083544\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-8.582205338335\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-1.058260083544\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.707106781187&{}:{}&0.707106781187&{}:{}&1.000000000000&. \end{alignedat} \]
6a (231)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.229058233121&{}:{}&-0.151553501366&{}:{}&-0.077504731755&. \end{alignedat} \]
6a (231)

Hiroyasu Kamo