In the Elements of Geometry, it is stated: "Two distinct points determine a line." In general, three distinct points determine $C_{2}^{3} = 3$ lines; however, if these three points are collinear, only one line is determined. On the coordinate plane, circle $\Gamma_{1}: x^{2} + y^{2} = 4$ intersects the two coordinate axes at 4 points, circle $\Gamma_{2}: x^{2} + y^{2} = 2$ intersects the line $x - y = 0$ at 2 points, and circle $\Gamma_{2}$ intersects the line $x + y = 0$ at 2 points. How many different lines can these 8 points determine?
(1) 12
(2) 16
(3) 20
(4) 24
(5) 28