Let P_1 P_2 ... P_18 be a regular 18-gon. Show that P_1 P_10, P_2 P_13, P_3 P_15 are concurrent.

Question

I've proved this with a diagram, but the question requires a rigorous proof.

Answer 1

one way is just to compute the equations of the lines joining the pairs of points, and show that they intersect in the same point.

On the unit circle, let
P1 = (1,0)
P2 = (cos pi/9,sin pi/9)
...

Answer 2

How do you find P3, P13, and P15? P10 is obviously (-1, 0), but I'm not sure how you got P2 and how to find the other three points