Question 55
a. There are $2n$ rays marked in a plane, with $n$ being a natural number. Given that no two marked rays have the same direction and no two marked rays have a common initial point, prove that there exists a line that passes through none of the initial points of the marked rays and intersects with exactly $n$ marked rays.
b. Would the claim still hold if the assumption that no two marked rays have a common initial point was dropped?
b. Would the claim still hold if the assumption that no two marked rays have a common initial point was dropped?