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]

\(\mathbf{7}\) \((222)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.063999515037&{}:{}&0.416000215539&{}:{}&0.520000269424&,\\B^\prime&{}\approx{}&0.583776452815&{}:{}&-0.556737207507&{}:{}&0.972960754692&,\\C^\prime&{}\approx{}&1.373016509412&{}:{}&1.830688679216&{}:{}&-2.203705188628&. \end{alignedat} \]
7 (222)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.248000646617\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}2.335105811260\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}5.492066037648\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.250000000000&{}:{}&0.333333333333&{}:{}&0.416666666667&. \end{alignedat} \]
7 (222)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.515433274099&{}:{}&0.334054901097&{}:{}&0.150511824804&. \end{alignedat} \]
7 (222)

Hiroyasu Kamo