Question

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of circle q.
using the compass measure between points s and n, draw an arc above line /, centered at n, intersecting the edge
use the compass to construct a circle centered at p through point q.
using the compass measure between points s and n, draw an arc to the right of line m, centered at t, intersecting
the edge of circle p.
use the compass to construct a circle centered at q through point p.

Explanation:

Step1: Analyze the options

• Option 1: Using the compass to construct a circle centered at \(Q\) through point \(P\) is a valid geometric construction step.
• Option 2: Using the compass to construct a circle centered at \(P\) through point \(Q\) is also a valid step.
• Option 3: Measuring between \(S\) and \(N\) with the compass and drawing an arc centered at \(N\) intersecting the edge of circle \(Q\) is a valid construction step.
• Option 4: Measuring between \(S\) and \(N\) with the compass and drawing an arc centered at \(T\) (which is not a relevant center for the basic construction of a perpendicular or parallel line in this context) is incorrect.

Answer:

Use the compass to construct a circle centered at \(Q\) through point \(P\) and Use the compass to construct a circle centered at \(P\) through point \(Q\) are correct construction steps.