Thank you for the feedback, Eric, Charley, Bill, Tom and Ross. Despite being raised in a woodworking family, I'm a router neophyte. But, the adage to divide and conquer seems fitting for this project. I did not route the sample in the images that I supplied, just tried to decode the construction method in order to create multiple picture frames in its likeness. The original frames a mirror attached to a dresser that has some MDF construction. Since I can't spot seams or joints, I assumed that the frame is of MDF with filler to even out the joints present. The back of the mirror appears to be one solid piece of MDF, but was likely laminated with the front-facing assembly. The paint is hiding a lot of information.
If I understand Eric correctly, creating an heirloom piece would involve some precision joinery, and I hadn't previously considered that possibility. Such a frame would be a beautiful architectural element in a Victorian house. (btw, I'm more jealous than you can imagine that Eric has the William Morris Red House to visit in Bexleyheath. My family visited Olana in the Hudson River Valley of New York last Summer, and we loved it.)
I can see now that my assumption that the corner triangles and circle could be routed out of a single piece of flat material was incorrect. The profile of the outside of the circle doesn't match the profile of the curved section of the triangles. My bad. The joint between the separately created triangles and the outside curve of the circle seems like the most demanding joint in the whole frame.
As Charley pointed out, the curved part of the triangles will need to use the same center as the circle, even though we're talking separate pieces of wood.
Thanks and regards,