50 In space, given four non-coplanar points $A, B, C, D$, the distance between any two points is different. Consider a plane $\alpha$ with the following property: three of the points $A, B, C, D$ are at the same distance from $\alpha$, and the fourth point is at a distance that is twice the distance of the other three points from $\alpha$. The number of such planes $\alpha$ is
A. 15
B. 23
C. 26
D. 32
50 D. There are three cases: (1) points $A, B, C, D$ are on the same side of $\alpha$; (2) among points $A, B, C, D$, 3 points are on one side of $\alpha$, and the 4th point is on the other side; (3) among the four points $A, B, C, D$, $\alpha$ has 2 points on each side. Plane $\alpha$ has a total of $4+4+4 C_{4}^{2}=32$.