I just acquired a 42” diameter solid pine kitchen table. I would like to cut and hinge each side parallel to the center cut where the leaf extension goes. It seems pretty straightforward but haven’t found any DIY plans to make this conversion. Photo1 is what I would like to achieve. Table is same style, except it has a center leaf insert, when installed, it appears as in photo2.
Your table has a skirt, and round folding leaf tables typically do not. My first questions would be, is the skirt required for the structural integrity of the piece? If not, are you willing to remove the skirt, if so, I start there.
After that, folding leaf tables are usually routers with a convex curve on the center leaf edge, and a concave curve on the folding leaf edge at the hinge. This is a design choice, but it adds to the effect of the finished table when the leaves are dropped, minimizing the visible gap at the hinge.
This cut has the potential to alter the round appearance of the table, as you will lose at least 1/8 inch from the blades kerf, and then if your router, you will likely lose a little more - just a consideration.
Finally, you'll want to consider the support mechanism that allows the drop leaves to be sturdy when up, and lets the drop when desired. This will be very dependant on the weight of the table's leaves, and how much room you have to work with underneath the table.
The simplest support would be a straight board with a swivel at its center, mounted to the edge of the inner seam. You could rotate it so it points outward and supports the drop leaf, and then swivel it in so it lets the leaf drop.