Derousseau's Generalization of the Malfatti circles

Angle Bisectors

Jump
[Guy]
[Lob & Richmond]
(0**)
(1**)
(2**)
(3**)

\begin{aligned}\overrightarrow{AA^{\prime}} &= \dfrac{1-{\sin\dfrac{\alpha}{2}}+{\sin\dfrac{\beta}{2}}+{\sin\dfrac{\gamma}{2}}+{\cos\dfrac{\alpha}{2}}+{\cos\dfrac{\beta}{2}}+{\cos\dfrac{\gamma}{2}}}{2\left(1+{\sin\dfrac{\alpha}{2}}+{\cos\dfrac{\beta}{2}}+{\cos\dfrac{\gamma}{2}}\right)}\overrightarrow{AX}\\\overrightarrow{BB^{\prime}} &= \dfrac{1+{\sin\dfrac{\alpha}{2}}-{\sin\dfrac{\beta}{2}}+{\sin\dfrac{\gamma}{2}}+{\cos\dfrac{\alpha}{2}}+{\cos\dfrac{\beta}{2}}+{\cos\dfrac{\gamma}{2}}}{2\left(1+{\cos\dfrac{\alpha}{2}}+{\sin\dfrac{\beta}{2}}+{\cos\dfrac{\gamma}{2}}\right)}\overrightarrow{BX}\\\overrightarrow{CC^{\prime}} &= \dfrac{1+{\sin\dfrac{\alpha}{2}}+{\sin\dfrac{\beta}{2}}-{\sin\dfrac{\gamma}{2}}+{\cos\dfrac{\alpha}{2}}+{\cos\dfrac{\beta}{2}}+{\cos\dfrac{\gamma}{2}}}{2\left(1+{\cos\dfrac{\alpha}{2}}+{\cos\dfrac{\beta}{2}}+{\sin\dfrac{\gamma}{2}}\right)}\overrightarrow{CX}\end{aligned}
Guy L & R $$\alpha$$ $$\beta$$ $$\gamma$$ $$X$$
0 (000) $$A$$ $$B$$ $$C$$ $$I$$
1 (002) $$-A$$ $$-B$$ $$2\pi-C$$ $$I$$
2 (020) $$-A$$ $$2\pi-B$$ $$-C$$ $$I$$
3 (022) $$A$$ $$2\pi+B$$ $$2\pi+C$$ $$I$$
4 (200) $$2\pi-A$$ $$-B$$ $$-C$$ $$I$$
5 (202) $$2\pi+A$$ $$B$$ $$2\pi+C$$ $$I$$
6 (220) $$2\pi+A$$ $$2\pi+B$$ $$C$$ $$I$$
7 (222) $$2\pi-A$$ $$2\pi-B$$ $$2\pi-C$$ $$I$$
0a (011) $$-A$$ $$\pi-B$$ $$\pi-C$$ $$I_A$$
1a (013) $$A$$ $$\pi+B$$ $$3\pi+C$$ $$I_A$$
2a (031) $$A$$ $$3\pi+B$$ $$\pi+C$$ $$I_A$$
3a (033) $$-A$$ $$3\pi-B$$ $$3\pi-C$$ $$I_A$$
4a (211) $$2\pi+A$$ $$\pi+B$$ $$\pi+C$$ $$I_A$$
5a (213) $$2\pi-A$$ $$\pi-B$$ $$3\pi-C$$ $$I_A$$
6a (231) $$2\pi-A$$ $$3\pi-B$$ $$\pi-C$$ $$I_A$$
7a (233) $$2\pi+A$$ $$3\pi+B$$ $$3\pi+C$$ $$I_A$$
0b (101) $$\pi-A$$ $$-B$$ $$\pi-C$$ $$I_B$$
1b (103) $$\pi+A$$ $$B$$ $$3\pi+C$$ $$I_B$$
2b (121) $$\pi+A$$ $$2\pi+B$$ $$\pi+C$$ $$I_B$$
3b (123) $$\pi-A$$ $$2\pi-B$$ $$3\pi-C$$ $$I_B$$
4b (301) $$3\pi+A$$ $$B$$ $$\pi+C$$ $$I_B$$
5b (303) $$3\pi-A$$ $$-B$$ $$3\pi-C$$ $$I_B$$
6b (321) $$3\pi-A$$ $$2\pi-B$$ $$\pi-C$$ $$I_B$$
7b (323) $$3\pi+A$$ $$2\pi+B$$ $$3\pi+C$$ $$I_B$$
0c (110) $$\pi-A$$ $$\pi-B$$ $$-C$$ $$I_C$$
1c (112) $$\pi+A$$ $$\pi+B$$ $$2\pi+C$$ $$I_C$$
2c (130) $$\pi+A$$ $$3\pi+B$$ $$C$$ $$I_C$$
3c (132) $$\pi-A$$ $$3\pi-B$$ $$2\pi-C$$ $$I_C$$
4c (310) $$3\pi+A$$ $$\pi+B$$ $$C$$ $$I_C$$
5c (312) $$3\pi-A$$ $$\pi-B$$ $$2\pi-C$$ $$I_C$$
6c (330) $$3\pi-A$$ $$3\pi-B$$ $$-C$$ $$I_C$$
7c (332) $$3\pi+A$$ $$3\pi+B$$ $$2\pi+C$$ $$I_C$$

Hiroyasu Kamo