19. Given a sphere of radius $R$. At a distance equal to $2R$ from the center of the sphere, a point $S$ is taken, and from it, all lines tangent to the sphere (i.e., having exactly one common point with it) are drawn. What does the union of these tangents represent? Calculate the area of the surface formed by the segments of the tangents from point $S$ to the points of tangency.
19. All tangents have a common point and are at the same distance from the center of the sphere. Therefore, the union of these tangents forms a surface of a cone of revolution. The length of the generatrix $l$ from point $S$ to the points of tangency is calculated using the Pythagorean theorem: $l^{2}=4 R^{2}-R^{2}, l=R \sqrt{3}$.

The radius $r$ of the corresponding cone is:

$$
r=l \sin 30^{\circ}=\frac{l}{2}=\frac{R}{2} \sqrt{3}
$$

The lateral surface area $S$ is determined by the formula:

$$
S=\pi r l, S=\frac{3 \pi R^{2}}{2}
$$