Derousseau's Generalization of the Malfatti circles

Barycentric Coordinates (2)


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

\(\mathbf{7b}\) \((323)\)

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

Hiroyasu Kamo