Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{2a}\) \((031)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.193437035124&{}:{}&0.334089318960&{}:{}&0.472473645917&,\\B^\prime&{}\approx{}&-4.361428811086&{}:{}&-0.806562964876&{}:{}&6.167991775962&,\\C^\prime&{}\approx{}&-0.041196100146&{}:{}&0.041196100146&{}:{}&1.000000000000&. \end{alignedat} \]
2a (031)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.472473645917\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}6.167991775962\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}0.058260083544\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.707106781187&{}:{}&0.707106781187&{}:{}&1.000000000000&. \end{alignedat} \]
2a (031)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.103298079348&{}:{}&0.143729978934&{}:{}&0.959568100414&. \end{alignedat} \]
2a (031)

Hiroyasu Kamo