Now I want to try this by placing the three cuts (chords) symmetrically so that they form a neat equilateral triangle at the center. I wonder if it is possible

Now I want to try this by placing the three cuts (chords) symmetrically so that they form a neat equilateral triangle at the center. I wonder if it is possible to make just the right cut so all pieces are "equal" (in area)? Is there a mathematical tool to make experiments like this graphically / visually? I define three cuts as lines that are offset by "x" from the center of the circle and as I vary the value of x from zero to r, the areas of each cut piece should be computed and plotted.