Derousseau's Generalization of the Malfatti circles

Barycentric Coordinates


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\(\mathbf{7b}\)   \((323)\)

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

Hiroyasu Kamo