Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{4a}\) \((211)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&2.303225372841&{}:{}&-0.477013593316&{}:{}&-0.826211779525&,\\B^\prime&{}\approx{}&3.911891463745&{}:{}&3.863703305156&{}:{}&-6.775594768901&,\\C^\prime&{}\approx{}&0.926746322053&{}:{}&-0.926746322053&{}:{}&1.000000000000&. \end{alignedat} \]
4a (211)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.826211779525\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-6.775594768901\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-1.605171715523\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.577350269190&{}:{}&0.577350269190&{}:{}&1.000000000000&. \end{alignedat} \]
4a (211)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.947384233015&{}:{}&-0.089526731899&{}:{}&-0.857857501116&. \end{alignedat} \]
4a (211)

Hiroyasu Kamo