there are thirty (30) points. To double check, add 1+2+3+4... till 19. Since you are dropping one line for every point connected to all the other lines, you just add the numbers consecutavely from 1 to the second last number of your point. The reason you DON'T add the last number is because you can't connect one point with itself.
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There are 91 lines.
there are 6 lines can pass through 4 noncollinear points.
There are 20 common points.
points : infinite lines : 4 vertices : 4
If the two lines are actually "on top of each other", they can have infinitely many points in common. If they are parallel, they have no points in common. If they are perpendicular, they have one point in common.