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]

\(\mathbf{4b}\) \((301)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.889140284973&{}:{}&-7.556561139894&{}:{}&9.445701424867&,\\B^\prime&{}\approx{}&0.289240056597&{}:{}&0.228693182409&{}:{}&0.482066760995&,\\C^\prime&{}\approx{}&0.037910698151&{}:{}&-0.050547597535&{}:{}&1.012636899384&. \end{alignedat} \]
4b (301)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}7.556561139894\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.385653408796\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.050547597535\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.750000000000&{}:{}&-1.000000000000&{}:{}&1.250000000000&. \end{alignedat} \]
4b (301)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.132215342733&{}:{}&-0.122482409476&{}:{}&0.990267066744&. \end{alignedat} \]
4b (301)

Hiroyasu Kamo