Detect perimetral walls of a room

Hi, I'm developing a building editor. Users can draw rooms by adding angles (vertices of the room) with a left click. Clicking on an existing angle closes the room and fills the floor by using the PointInPolygon algorithm. Let me illustrate the problem. I have this room.

 #-----------#
 |           |
 |           |
 |     #-----#
 |     |
 |     |
 |     |
 #-----#

Now I want to create another room by connecting two of the vertices like this:

 #-----------#
 |           |
 |           |
 |     V--A--X < first click
 |     |     |
 |     B     | <--new room
 |     |     |
 #-----Y-----#
       ^
   second click

I need to detect the vertex V and the edges A and B. I tried to implement the convex hull algorithm to find the external walls, but there are degenerated cases where those edges are interior walls... I even tried the Dijstra's algorithm to find the shortest path between X and Y, but again there are degenerated cases like this:

  first click
       v
       X----------# < second click
       |          |
 #-----#-----#    |
 |     |     |    | 
 |     |     |    | <--new room
 |     |     |    |
 #-----#-----#    |
       |          |
       Y----------# < third click
       ^
 fourth click

How should I approach this problem?