Derousseau's Generalization of the Malfatti circles

Barycentric Coordinates (1)


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

\(\mathbf{7c}\) \((332)\)

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

Hiroyasu Kamo