Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{2b}\) \((121)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&3.863703305156&{}:{}&3.911891463745&{}:{}&-6.775594768901&,\\B^\prime&{}\approx{}&-0.477013593316&{}:{}&2.303225372841&{}:{}&-0.826211779525&,\\C^\prime&{}\approx{}&-0.926746322053&{}:{}&0.926746322053&{}:{}&1.000000000000&. \end{alignedat} \]
2b (121)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-6.775594768901\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.826211779525\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-1.605171715523\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.577350269190&{}:{}&-0.577350269190&{}:{}&1.000000000000&. \end{alignedat} \]
2b (121)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.089526731899&{}:{}&1.947384233015&{}:{}&-0.857857501116&. \end{alignedat} \]
2b (121)

Hiroyasu Kamo