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

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