Connect vertices where they would meet, not fill? Lets say I have a plane, and I extrude two edges, it would produce a gap. I would like to fill this gap by using the projected intersection of the new outer edges. Shown in the right most example of the image below:



I can extrude the two vertices and fill the area, making the desired outcome. If I had used F to fill before I've made the vertices meet, the result would be a square with diagonal edges (the empty area would be filled and turned into a triangle, not a square).

For my situation, I am trying to do the same, except I am using a circle. If I simply hit F to join the two vertices I get the result seen on 3.
How can I connect the two vertices where they meet (shown in 4). Are there any tools to get the intersection or fill it automatically?
You might want to try the tinyCAD addon.

Select the two extruded edges then choose w->TinyCAD->VTX Auto and you will get a vertex joining the two where they would intersect.