Derousseau's Generalization of the Malfatti circles

\(A=60\degree\), \(B=60\degree\), \(C=60\degree\)


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\(\displaystyle\overrightarrow{AA^\prime}=\frac{3-\sqrt{3}}2\overrightarrow{AI}\),   \(\displaystyle\overrightarrow{BB^\prime}=\frac{3-\sqrt{3}}2\overrightarrow{BI}\),   \(\displaystyle\overrightarrow{CC^\prime}=\frac{3-\sqrt{3}}2\overrightarrow{CI}\).
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Hiroyasu Kamo