Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{6b}\) \((321)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&3.513669746063&{}:{}&6.068535592272&{}:{}&-8.582205338335&,\\B^\prime&{}\approx{}&-0.041196100146&{}:{}&1.099456183690&{}:{}&-0.058260083544&,\\C^\prime&{}\approx{}&-0.748302881333&{}:{}&0.748302881333&{}:{}&1.000000000000&. \end{alignedat} \]
6b (321)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-8.582205338335\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.058260083544\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-1.058260083544\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.707106781187&{}:{}&-0.707106781187&{}:{}&1.000000000000&. \end{alignedat} \]
6b (321)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.151553501366&{}:{}&1.229058233121&{}:{}&-0.077504731755&. \end{alignedat} \]
6b (321)

Hiroyasu Kamo