Derousseau's Generalization of the Malfatti circles

Barycentric Coordinates (2)


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

\(\mathbf{0a}\) \((011)\)

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

Hiroyasu Kamo