Adam has a circle of radius 1 centered at the origin.
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First, he draws 6 segments from the origin to the boundary of the circle, which splits the upper (positive y) semicircle into 7 equal pieces.
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Next, starting from each point where a segment hit the circle, he draws an altitude to the x-axis.
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Finally, starting from each point where an altitude hit the x-axis, he draws a segment directly away from the bottommost point of the circle (0,-1), stopping when he reaches the boundary of the circle.
What is the product of the lengths of all 18 segments Adam drew?
