Derousseau's Generalization of the Malfatti circles

Angle Bisectors (2)


[Other solutions]
[Guy]
[Lob & Richmond]

\(\mathbf{3b}\) \((123)\)

\[\begin{aligned}\overrightarrow{AA^{\prime}}&=-\dfrac{\cos\dfrac{A}{4}\sin\dfrac{B}{4}\sin\dfrac{\pi-{C}}{4}}{\sqrt{2}\cos\dfrac{\pi-{A}}{4}\cos\dfrac{\pi-{B}}{4}\sin\dfrac{C}{4}}\overrightarrow{A{I_B}},\\\overrightarrow{BB^{\prime}}&=-\dfrac{\cos\dfrac{\pi-{A}}{4}\cos\dfrac{\pi-{B}}{4}\sin\dfrac{\pi-{C}}{4}}{\sqrt{2}\cos\dfrac{A}{4}\sin\dfrac{B}{4}\sin\dfrac{C}{4}}\overrightarrow{B{I_B}},\\\overrightarrow{CC^{\prime}}&=-\dfrac{\cos\dfrac{\pi-{A}}{4}\sin\dfrac{B}{4}\sin\dfrac{C}{4}}{\sqrt{2}\cos\dfrac{A}{4}\cos\dfrac{\pi-{B}}{4}\sin\dfrac{\pi-{C}}{4}}\overrightarrow{C{I_B}}.\end{aligned}\]

Hiroyasu Kamo