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]

\(\mathbf{0c}\) \((110)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.137704095259&{}:{}&0.550816381038&{}:{}&-0.688520476297&,\\B^\prime&{}\approx{}&0.467232496600&{}:{}&1.311488331067&{}:{}&-0.778720827667&,\\C^\prime&{}\approx{}&3.564755078384&{}:{}&4.753006771179&{}:{}&-7.317761849563&. \end{alignedat} \]
0c (110)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.275408190519\overrightarrow{AI_C},\\\overrightarrow{BB^\prime}&\approx{}0.311488331067\overrightarrow{BI_C},\\\overrightarrow{CC^\prime}&\approx{}2.376503385590\overrightarrow{CI_C}. \end{aligned} \] \[ \begin{alignedat}{4} I_C&{}\approx{}&1.500000000000&{}:{}&2.000000000000&{}:{}&-2.500000000000&. \end{alignedat} \]
0c (110)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&1.078042283606&{}:{}&1.307293031736&{}:{}&-1.385335315343&. \end{alignedat} \]
0c (110)

Hiroyasu Kamo