Derousseau's Generalization of the Malfatti circles

\(a:b:c=231:250:289\).


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\(\displaystyle\overrightarrow{AA^\prime}=\frac{20}{11}\overrightarrow{AI}\),   \(\displaystyle\overrightarrow{BB^\prime}=\frac{11}5\overrightarrow{BI}\),   \(\displaystyle\overrightarrow{CC^\prime}=\frac{55}{16}\overrightarrow{CI}\).
\(\displaystyle A^\prime=-\frac3{11}:\frac{500}{847}:\frac{578}{847}\),   \(\displaystyle B^\prime=\frac{33}{50}:-\frac{17}{35}:\frac{289}{350}\),   \(\displaystyle C^\prime=\frac{33}{32}:\frac{125}{112}:-\frac{257}{224}\).
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Hiroyasu Kamo