Construction 3

Geometry Level 2

Let \(r\) be a randomly chosen positive rational number, less than 1.

You have a stiff compass, such that you are only allowed to construct a circle with a radius \(r\). Furthermore you have a straightedge. Is it possible to construct a perpendicular from a given point to a line?

Note: To make the task more difficult, assume that the distance between the line and the point is more than 10.

Bonus: Reduce the steps (you used for the construction) under 20.

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