Derousseau's Generalization of the Malfatti circles

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


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

\(\mathbf{7b}\) \((323)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&5.385410681680&{}:{}&5.990582397203&{}:{}&-10.375993078883&,\\B^\prime&{}\approx{}&-0.007454734077&{}:{}&1.020366712256&{}:{}&-0.012911978179&,\\C^\prime&{}\approx{}&-0.605171715523&{}:{}&0.605171715523&{}:{}&1.000000000000&. \end{alignedat} \]
7b (323)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-10.375993078883\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.012911978179\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-1.048188158589\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.577350269190&{}:{}&-0.577350269190&{}:{}&1.000000000000&. \end{alignedat} \]
7b (323)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.028756245388&{}:{}&1.062356189989&{}:{}&-0.033599944601&. \end{alignedat} \]
7b (323)

Hiroyasu Kamo