Find the Intersection of Two Straight Lines

Geometric Construction with the Compass Alone

Find the intersection point of two lines each given by a pair of points - AB and CD, respectively.

Solution

The solution takes several steps:

  1. Construct C1 and D1 symmetric to C and D with respect to AB (Problem #2). The required point X can be found in the intersection of CD and C1D1.
  2. Complete the parallelogram CC1D1E (Problem #6).
  3. Find x from DE/DD1 = CD/x (Problem #10).
  4. Draw two circles of radius x centered at D and D1. The required point X lies in the intersection of the two circles.

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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