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]

\(\mathbf{5b}\) \((303)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.651429130069&{}:{}&-1.394283479725&{}:{}&1.742854349656&,\\B^\prime&{}\approx{}&0.268955349076&{}:{}&0.282785735798&{}:{}&0.448258915126&,\\C^\prime&{}\approx{}&0.078480113194&{}:{}&-0.104640150925&{}:{}&1.026160037731&. \end{alignedat} \]
5b (303)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.394283479725\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}0.358607132101\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}0.104640150925\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.750000000000&{}:{}&-1.000000000000&{}:{}&1.250000000000&. \end{alignedat} \]
5b (303)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.226775075125&{}:{}&-0.109135891114&{}:{}&0.882360815989&. \end{alignedat} \]
5b (303)

Hiroyasu Kamo