Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{4b}\) \((301)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.806562964876&{}:{}&-4.361428811086&{}:{}&6.167991775962&,\\B^\prime&{}\approx{}&0.334089318960&{}:{}&0.193437035124&{}:{}&0.472473645917&,\\C^\prime&{}\approx{}&0.041196100146&{}:{}&-0.041196100146&{}:{}&1.000000000000&. \end{alignedat} \]
4b (301)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}6.167991775962\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.472473645917\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.058260083544\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.707106781187&{}:{}&-0.707106781187&{}:{}&1.000000000000&. \end{alignedat} \]
4b (301)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.143729978934&{}:{}&-0.103298079348&{}:{}&0.959568100414&. \end{alignedat} \]
4b (301)

Hiroyasu Kamo