Derousseau's Generalization of the Malfatti circles

\(A=45\degree\), \(B=45\degree\), \(C=90\degree\)


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