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It is not at all clear from previous posts that you cannot draw chords of fixed length inside a circle. You said you can't do trial and error, and this is not. You fix one mark on a circle and rotate until another mark is on the circumference. I admit i didn't read that the ruler had infinite...

Easy, provided the marking are actually small enough for you to mark around the circle. draw a line AB with A clockwise from B. Let AC be a 1 unit chord with C clockwise from A, and BD be 1 unit with D anticlockwise from B. Let EC be a 1 unit chord with E clockwise from C, and FD be 1 unit...