Derousseau's Generalization of the Malfatti circles

Barycentric Coordinates


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\(\mathbf{1c}\)   \((112)\)

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

Hiroyasu Kamo