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:

1. One centered at C with radius AB
2. 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)

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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