Drop a Perpendicular to a Line from a Point

Geometric Construction with the Compass Alone

A segment AB is given by its end points A and B. Find a point C such that AC is perpendicular to AB.


Before attempting this problem you should look into the first one.

With an arbitrary radius R ≥ AB draw two circles with centers at A and B. Let O be one of the points of intersection. With the center O and the same radius R draw a circle and then use the first problem to find the point C opposite the point B on this circle. Then AC is perpendicular to AB.

Problems (Use a compass only)

  1. Multiply a Line Segment by a Whole Number
  2. Reflect a Point in a Line Sgement
  3. Cross a Circle by a Line Segment
  4. Drop a Perpendicular to a Line from a Point
  5. Detect Collinearity
  6. Complete a Parallelogram
  7. Bisect an Arc
  8. Find the Points of Intersection of a Circle with a Line Segment
  9. Build a Square on a Given Side
  10. Find the Fourth Proportional of Three Lengths
  11. Find the Intersection of Two Straight Lines
  12. Divide a Line Segment into a Whole Number of Parts
  13. Find the Center of a Given Circle
  14. Bisect a given line
  15. Mascheroni Construction of a Regular Pentagon
  16. A Compass Only Construction - A Chord Tangent to an Inner circle

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