Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{1c}\) \((112)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.000000000000&{}:{}&-1.366025403784&{}:{}&2.366025403784&,\\B^\prime&{}\approx{}&-1.366025403784&{}:{}&-0.000000000000&{}:{}&2.366025403784&,\\C^\prime&{}\approx{}&-13.522257448825&{}:{}&-13.522257448825&{}:{}&28.044514897649&. \end{alignedat} \]
1c (112)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.366025403784\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}-0.366025403784\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}-3.623277963258\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&3.732050807569&{}:{}&3.732050807569&{}:{}&-6.464101615138&. \end{alignedat} \]
1c (112)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-1.762033366018&{}:{}&-1.762033366018&{}:{}&4.524066732036&. \end{alignedat} \]
1c (112)

Hiroyasu Kamo