Derousseau's Generalization of the Malfatti circles

\(A=30\degree\), \(B=30\degree\), \(C=120\degree\).


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

\(\mathbf{0c}\) \((110)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.577350269190&{}:{}&0.788675134595&{}:{}&-1.366025403784&,\\B^\prime&{}\approx{}&0.788675134595&{}:{}&1.577350269190&{}:{}&-1.366025403784&,\\C^\prime&{}\approx{}&13.790206641256&{}:{}&13.790206641256&{}:{}&-26.580413282512&. \end{alignedat} \]
0c (110)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.211324865405\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.211324865405\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}3.695074732983\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&3.732050807569&{}:{}&3.732050807569&{}:{}&-6.464101615138&. \end{alignedat} \]
0c (110)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.830023832870&{}:{}&1.830023832870&{}:{}&-2.660047665740&. \end{alignedat} \]
0c (110)

Hiroyasu Kamo