OpenGL Coordinates

I have created a 2D oval type shape from lying in the xz plane at y=0. I stored the x and z coordinates in an array from an infile, and then just used glBegin(GL_LINE_LOOP); to draw the shape. Now, I need to be able to fan out from the center of the “kind of oval” shape every 30 degrees until I touch the edge of my shape and I need the coordinates of wherever I hit the shape for each spot where I fanned out. How can I do this?