# 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:

- Construct C
_{1}and D_{1}symmetric to C and D with respect to AB (Problem #2). The required point X can be found in the intersection of CD and C_{1}D_{1}. - Complete the parallelogram CC
_{1}D_{1}E (Problem #6). - Find x from DE/DD
_{1}= CD/x (Problem #10). - Draw two circles of radius x centered at D and D
_{1}. 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

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