If the program is presented with X and Y coordinates, how do I get the program to connect those dots to form a shape similar to a circle?

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algorithm

If the program is presented with X and Y coordinates, how do I get the program to connect those dots to form a shape similar to a circle? This means that the program is trying to create a shape by connecting those dots. What I want to know: How do I determine which dots to connect to form the circle(or the shape closest to a circle).
I'm not looking for any specific code, just the algorithm. Thanks:)

Example:

This is the visual representation of the input(the coordinates)
The program will use these coordinates to create a shape by connecting them. The output should show which dots where connected to form that shape. This shape should go through all the dots and still be the closest possible shape(through the dots) to a circle/have the largest possible surface area.
visual representation of the output
The output of this example should be AB,BC,CX,XY,YZ,ZA

What I have tried:

I've tried comparing the distances between the dots to see what the shortest path through all the dots are that end at the starting point and that seems give a good result. I am sure however that there is a more effective algorithm.