Derousseau's Generalization of the Malfatti circles

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


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\(\displaystyle\overrightarrow{AA^\prime}=\frac{5+3\sqrt{3}}6\overrightarrow{AI_A}\),   \(\displaystyle\overrightarrow{BB^\prime}=\frac{-1+\sqrt{3}}2\overrightarrow{BI_A}\),   \(\displaystyle\overrightarrow{CC^\prime}=\frac{-1+\sqrt{3}}2\overrightarrow{CI_A}\).
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Hiroyasu Kamo