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.
The solution takes several steps:
- 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.
- Complete the parallelogram CC1D1E (Problem #6).
- Find x from DE/DD1 = CD/x (Problem #10).
- 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)
- Multiply a Line Segment by a Whole Number
- Reflect a Point in a Line Sgement
- Cross a Circle by a Line Segment
- Drop a Perpendicular to a Line from a Point
- Detect Collinearity
- Complete a Parallelogram
- Bisect an Arc
- Find the Points of Intersection of a Circle with a Line Segment
- Build a Square on a Given Side
- Find the Fourth Proportional of Three Lengths
- Find the Intersection of Two Straight Lines
- Divide a Line Segment into a Whole Number of Parts
- Find the Center of a Given Circle
- Bisect a given line
- Mascheroni Construction of a Regular Pentagon
- A Compass Only Construction - A Chord Tangent to an Inner circle