Derousseau's Generalization of the Malfatti circles

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


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\(\displaystyle\overrightarrow{AA^\prime}=\frac47\overrightarrow{AI}\),   \(\displaystyle\overrightarrow{BB^\prime}=\frac79\overrightarrow{BI}\),   \(\displaystyle\overrightarrow{CC^\prime}=\frac{63}{16}\overrightarrow{CI}\).
\(\displaystyle A^\prime=\frac35:\frac{100}{539}:\frac{578}{2695}\),   \(\displaystyle B^\prime=\frac7{30}:\frac{47}{99}:\frac{289}{990}\),   \(\displaystyle C^\prime=\frac{189}{160}:\frac{225}{176}:-\frac{2569}{1760}\).
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Hiroyasu Kamo