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]

\(\mathbf{1}\) \((002)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.167552905630&{}:{}&0.518912402502&{}:{}&0.648640503128&,\\B^\prime&{}\approx{}&0.468000242482&{}:{}&-0.248000646617&{}:{}&0.780000404136&,\\C^\prime&{}\approx{}&0.023430099995&{}:{}&0.031240133326&{}:{}&0.945329766679&. \end{alignedat} \]
1 (002)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.556737207507\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}1.872000969926\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}0.093720399979\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.250000000000&{}:{}&0.333333333333&{}:{}&0.416666666667&. \end{alignedat} \]
1 (002)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.074292983178&{}:{}&0.101894297245&{}:{}&0.823812719577&. \end{alignedat} \]
1 (002)

Hiroyasu Kamo