Build a Square on a Given Side

Geometric Construction with the Compass Alone

Build a square with a given side AB.


Using Problem #4 first construct CA perpendicular to AB. Draw the circle A(B) of radius AB and center A and another centered at C and intersecting the former in points, say, M and N. We are given then circle A(B) and an arc MN that can be bisected following the construction in Problem #7. Both thus found points will lie on AC at the distance from A equal to AB. Denote one of them D: AD = AB and ∠BAD = 90°.

Swing two arcs of radius AB - one centered at D, another at B. The arcs will intersect at A and another point, say, E. The quadrilateral ADEB is a square.

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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