Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{4c}\) \((310)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&4.761972627396&{}:{}&9.082205338335&{}:{}&-12.844177965731&,\\B^\prime&{}\approx{}&0.160435348784&{}:{}&1.066454497351&{}:{}&-0.226889846135&,\\C^\prime&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&. \end{alignedat} \]
4c (310)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}5.320232710939\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.093980851434\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}0.292893218813\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.707106781187&{}:{}&1.707106781187&{}:{}&-2.414213562373&. \end{alignedat} \]
4c (310)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.477469104681&{}:{}&1.069449055997&{}:{}&-0.546918160678&. \end{alignedat} \]
4c (310)

Hiroyasu Kamo