Derousseau's Generalization of the Malfatti circles

The Smallest Eisenstein Triangle

\(C=120\degree\).   \(a:b:c=3:5:7\).


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

\(\mathbf{2b}\) \((121)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&3.115510644079&{}:{}&5.288776610198&{}:{}&-7.404287254278&,\\B^\prime&{}\approx{}&-0.635089355133&{}:{}&3.116964517109&{}:{}&-1.481875161976&,\\C^\prime&{}\approx{}&-0.692638588899&{}:{}&1.154397648165&{}:{}&0.538240940734&. \end{alignedat} \]
2b (121)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-5.288776610198\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-1.058482258555\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-1.154397648165\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.600000000000&{}:{}&-1.000000000000&{}:{}&1.400000000000&. \end{alignedat} \]
2b (121)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.106249659921&{}:{}&2.607013108030&{}:{}&-1.500763448109&. \end{alignedat} \]
2b (121)

Hiroyasu Kamo