# 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)

- Multiply a Line Segment by a Whole Number
- Reflect a Point in a Line Sgement
- Cross a Circle by a Line Segment
- Drop a Perpendicular to a Line from a Point
- Detect Collinearity
- Complete a Parallelogram
- Bisect an Arc
- Find the Points of Intersection of a Circle with a Line Segment
- Build a Square on a Given Side
- Find the Fourth Proportional of Three Lengths
- Find the Intersection of Two Straight Lines
- Divide a Line Segment into a Whole Number of Parts
- Find the Center of a Given Circle
- Bisect a given line
- Mascheroni Construction of a Regular Pentagon
- A Compass Only Construction - A Chord Tangent to an Inner circle

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