Constrained Delaunay Triangulation: find all faces inside circle

[Tazdraperm]

So the title is it all. I have CDT that I use for pathfinding. Some faces are marked as impassable. I need a way to detect if an agent (circle with specific radius) is colliding with impassable face.
The best I can think of is using multiple line_walk's, but this is obviously not a very good solution