Derousseau's Generalization of the Malfatti circles

Angle Bisectors (2)


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

\(\mathbf{3a}\) \((033)\)

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

Hiroyasu Kamo