# Complete a Parallelogram

### Geometric Construction with the Compass Alone

Given three points A, B and C. C is known to lie outside the straight line AB. Complete the parallelogram ABCD.

## Solution

Draw two circles:

- One centered at C with radius AB
- Another centered at B with the radius AC

D is one of the intersection points of the two circles. How many solutions has the problem?

### 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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