Derousseau's Generalization of the Malfatti circles

Barycentric Coordinates


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\(\mathbf{3b}\)   \((123)\)

\[\begin{aligned}A^{\prime} &= \left(4\sec^2\dfrac{\pi-{A}}{4}\sin^2\dfrac{B}{4}\sin^2\dfrac{\pi-{C}}{4}-1\right){\sin{A}}:-{\sin{B}}:{\sin{C}}\\B^{\prime} &= {\sin{A}}:-\left(4\cos^2\dfrac{\pi-{A}}{4}\csc^2\dfrac{B}{4}\sin^2\dfrac{\pi-{C}}{4}-1\right){\sin{B}}:{\sin{C}}\\C^{\prime} &= {\sin{A}}:-{\sin{B}}:\left(4\cos^2\dfrac{\pi-{A}}{4}\sin^2\dfrac{B}{4}\csc^2\dfrac{\pi-{C}}{4}-1\right){\sin{C}}\end{aligned}\]

Hiroyasu Kamo