Find the Points of Intersection of a Circle with a Line Segment

Geometric Construction with the Compass Alone

A circle is given by its radius R and the center O that lies on AB. Find the points of intersection of the circle with the segment AB.

Solution

From the point A swing an arc of arbitrary radius intersecting the given circle. Let C and D be the points of intersection. Using Problem #7 bisect two arcs CD of the original circle.

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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