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We only need one of the top two arcs, right?

Good. Now the last small problem: you need to find out a point at the top of upper arc - we cannot draw the top horizontal line like that. We can draw a line only by connecting 2 points.

No, worse.

Try to find out point P first:

better to show how you can find that point with straightedge(ruler) and compass, maybe using a different color

You got P by drawing a perpendicular of the botton horizontal line through Q, right?

How can you make a perpendicular like that?

Originally, we have L1 and P1. Based on your cool solution, the following steps make sense to me:

step1: get an arbitrary point P2 on L1
step2: make a perpendicular of L1 through P2, we get L3
step3: put your compass at point P2 and cut L3 at P3
step4: draw a line through P1 and P3 we are done

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