Drag the third vertex, C, anywhere outside circles centered at A and B and the corresponding third vertices of similar triangles sharing side AB will move correspondingly.

Notice that when C is on one of the isosceles curves (blue), the number of similar triangles drops to 3. The way this construction was done, if C is dragged onto the circle centered at B then the point that should be indicated on the circle centered at A is dropped -- this is not intentional.

This arrangment ignores the other similar triangles that can be found by reflection in the line through A and B.