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Problem 618

Using a straight edge only, construct the perpendicular to a given diameter of a circle from any point off the diameter.

Expert verified

To construct the perpendicular to a given diameter of a circle from any point off the diameter using a straight edge only, follow these steps:
1. Draw the circle and its diameter, labeling endpoints as A and B.
2. Choose a point outside the diameter, label it as C.
3. Connect C to A and C to B using straight edge.
4. Construct midpoints M and N of segments CA and CB, respectively.
5. Draw a line through points M and N, extending beyond the circle.
6. Find the intersection point D of this line with the circle.
7. Connect point C to D, which is the perpendicular to diameter AB.

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