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]

\(\mathbf{0b}\) \((101)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.921519886806&{}:{}&-0.313920452774&{}:{}&0.392400565968&,\\B^\prime&{}\approx{}&1.194570142487&{}:{}&-2.185520379965&{}:{}&1.990950237478&,\\C^\prime&{}\approx{}&0.348570869931&{}:{}&-0.464761159908&{}:{}&1.116190289977&. \end{alignedat} \]
0b (101)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.313920452774\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}1.592760189982\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.464761159908\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.750000000000&{}:{}&-1.000000000000&{}:{}&1.250000000000&. \end{alignedat} \]
0b (101)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.736018478900&{}:{}&-0.681837030797&{}:{}&0.945818551897&. \end{alignedat} \]
0b (101)

Hiroyasu Kamo