Multiply a Line Segment by a Whole Number

Geometric Construction with the Compass Alone

A segment AB is given by its end points A and B. Construct segments 2, 3, 4, etc. times larger than AB.

Solution

Swing an arc with the center B of radius AB. With the same radius swing first an arc with the center A until it intersects the first arc at a point C. With C as the center draw and arc to obtained the point D. With D as the center draw and arc to obtained the point E. The segment AE is twice as big as the segment AB. In a similar fashion segment BE can be extended to EF, twice as big a segment as BE. Then AF is three times as long as AB. Etc.

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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