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]

\(\mathbf{7b}\) \((323)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.848570869931&{}:{}&3.394283479725&{}:{}&-4.242854349656&,\\B^\prime&{}\approx{}&-0.018955349076&{}:{}&1.050547597535&{}:{}&-0.031592248460&,\\C^\prime&{}\approx{}&-0.578480113194&{}:{}&0.771306817591&{}:{}&0.807173295602&. \end{alignedat} \]
7b (323)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-3.394283479725\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.025273798768\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-0.771306817591\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.750000000000&{}:{}&-1.000000000000&{}:{}&1.250000000000&. \end{alignedat} \]
7b (323)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.069743418466&{}:{}&1.159367009379&{}:{}&-0.089623590914&. \end{alignedat} \]
7b (323)

Hiroyasu Kamo