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.