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Ah. So "it's easy to draw what appear to be the circle segments, but aren't".

You see when he said "the circle segments" I thought he meant "the circle segments" instead of "straight lines that do not belong to the circles we were discussing earlier".

If you glue those two pieces back together you get a single unbroken loop, not two circles. So, no, its not "easy to draw the circle segments so they don't intersect" because the lines won't form two circles