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.

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