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]

\(\mathbf{5}\) \((202)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.873016509412&{}:{}&0.056437106928&{}:{}&0.070546383660&,\\B^\prime&{}\approx{}&0.738284950003&{}:{}&-0.968759866674&{}:{}&1.230474916671&,\\C^\prime&{}\approx{}&0.563999515037&{}:{}&0.751999353383&{}:{}&-0.315998868420&. \end{alignedat} \]
5 (202)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.169311320784\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}2.953139800010\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}2.255998060148\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.250000000000&{}:{}&0.333333333333&{}:{}&0.416666666667&. \end{alignedat} \]
5 (202)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.752939500973&{}:{}&0.027194409752&{}:{}&0.219866089275&. \end{alignedat} \]
5 (202)

Hiroyasu Kamo