I have taken a regular hendecagon (11-sided polygon) and added extensions to each of the sides so that they intersect as shown. Wherever it is possible to connect two of these intersection points with a horizontal line I have done so, and denoted them A to P. (Except for the magenta dashed line passing through the horizontal side of the hendecagon, which has several intersection points on it, but can be ignored for the purposes of this puzzle).

Some of these lines A to P have a very curious property, that if you form a circle whose diameter exactly coincides with said line, the circle will pass exactly through the midpoints of two of the sides of the original hendecagon.

Can you list all those lines which have this property?