Theres a faster construction

Geometry Level 5

Given a line \(l\) and a point \(P\) on \(l\), what is the minimium number of uses of a straightedge or compass in order to construct a line through \(P\) perpendicular to \(l\)?


All terminology in this question is explained in the first note of my straightedge and compass set. More straightedge and compass constructions can be found there.

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