# Build a Square on a Given Side

### Geometric Construction with the Compass Alone

Build a square with a given side AB.

## Solution

Using Problem #4 first construct CA perpendicular to AB. Draw the circle A(B) of radius AB and center A and another centered at C and intersecting the former in points, say, M and N. We are given then circle A(B) and an arc MN that can be bisected following the construction in Problem #7. Both thus found points will lie on AC at the distance from A equal to AB. Denote one of them D:

Swing two arcs of radius AB - one centered at D, another at B. The arcs will intersect at A and another point, say, E. The quadrilateral ADEB is a square.

### 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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