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.

Solution

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

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