Derousseau's Generalization of the Malfatti circles

The Smallest Pythagorean Triangle

\(C=90\degree\).   \(a:b:c=3:4:5\).


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

\(\mathbf{6a}\) \((231)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.091524521636&{}:{}&-0.040677565172&{}:{}&-0.050846956465&,\\B^\prime&{}\approx{}&4.097262605646&{}:{}&3.731508403764&{}:{}&-6.828771009409&,\\C^\prime&{}\approx{}&0.782507527261&{}:{}&-1.043343369682&{}:{}&1.260835842420&. \end{alignedat} \]
6a (231)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-0.061016347758\overrightarrow{AI_A},\\\overrightarrow{BB^\prime}&\approx{}-8.194525211291\overrightarrow{BI_A},\\\overrightarrow{CC^\prime}&\approx{}-1.565015054523\overrightarrow{CI_A}. \end{aligned} \] \[ \begin{alignedat}{4} I_A&{}\approx{}&-0.500000000000&{}:{}&0.666666666667&{}:{}&0.833333333333&. \end{alignedat} \]
6a (231)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.210475104788&{}:{}&-0.149829035022&{}:{}&-0.060646069766&. \end{alignedat} \]
6a (231)

Hiroyasu Kamo