
How to construct the horizontal and vertical centerlines of a given circle?

1. 
 Start with the given circle.


2. 
 Choose an arbitrary point on the circle in a horizontal direction relative to the center of the circle.
"Horizontal" has no real meaning within rulerandcompass constructions, neither do "vertical", "left", "right". They only help to give orientation to the construction. The choice of the point, therefore, is indeed arbitrary. The only restriction here is, that horizontal and vertical must be (mutual) perpendicular.


3. 
 Draw the connection between point 2 and the center of circle 1, and extend it until it intersects the circle a second time.


4. 
 The connection between both intersections with circle 1 is the horizontal centerline.
The normal term for such a line is "diameter", but diameter is also used to denote the length of the given line. I therefore prefer the term centerline to emphasis the line itself, not its length.


5. 
 Use the
construction of a perpendicular bisector, to construct a line through the center of circle 1 and perpendicular to line 4.


6. 
 The segment of line 5 between the intersections with circle 1 (inclusive) is the vertical centerline.


7. 
 So, lines 4 and 6 are the horizontal and vertical centerlines to be constructed.

