Solving for Parameter Restrictions in Q2: Geometric Help Needed

[hedipaldi]

Homework Statement

The problem is Q2 in the attached

Homework Equations

The Attempt at a Solution

I am trying to determine the rigion of parameters for each number of crosses,where x and y are the distances of the center of cross from the closest line respectively,and θ is the acute angle.I need some help with this.My problem is in determining the geometric restrictions for each number of intersections,rather than the probability computatons.

 

[haruspex]

Can the cross intersect more than one line?

 

[hedipaldi]

Yes,it can.

 

[haruspex]

Yes,it can.

I intended that as a rhetorical question. The cross is two unit-length needles joined at their mid-points; the lines are unit distance apart. The cross can intersect the same line with both needles, but I fail to see how it can intersect two lines.