Detect Collinearity

Geometric Construction with the Compass Alone

Determine whether three given points A, B, C lie on the same line.

Solution

Pick up an arbitrary point D outside the line AB. Let D' be symmetric to D with respect to AB (see problem #2). Then C lies on the line AB if and only if CD = CD'.

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
16. A Compass Only Construction - A Chord Tangent to an Inner circle

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