In my opinion, you should redo it like this :
Add Mesh -> Circle and set the vertices to 72
Extrude the circle and press S to scale it so you obtain
Now select that vertice in the bottom of the circle and press SHIFT+D to duplicate it
now extrude on the correct axis (depends on how your circle is oriented) that vertice to obtain this edge that is separated from the circle.
Extrude on both side to obtain this
(you can dissolve the edge in the center of that plane, it will not serve any purpose now)
Now move a bit your plane so it’s a bit inside the circle like this :
Get on top view of your circle, make sure only your plane is selected (and the 3D cursor is at the center of the circle, if it’s not select only the circle and press SHIFT+S -> Cursor to Selected)
In the T panel (the panel to the left of the 3D View) click on the Spin button
Either in the operator menu (the panel on the bottom of the T Panel) or press F6 to make it popup and set it up like this :
Once done, select all and press W -> Remove Doubles as the original plane will be duplicated on top of itself
Now you will need the excellent and extremely usefull Tiny CAD VTX addon
To enable it if you don’t have enabled it already, go to File -> User Preferences -> Addons
In the Mesh category enable “Edge Tools : Tiny CAD VTX”
Back into the 3D view by example select those 2 edges
Press W -> Edges X Intersection
Select now those 2 edges
Press W -> Edges X Intersection
Select those now useless edges and press X -> Edges to delete them :
Then remake the faces
Doing it this way you should obtain in the end your desired model