# Find the Points of Intersection of a Circle with a Line Segment

### Geometric Construction with the Compass Alone

A circle is given by its radius R and the center O that lies on AB. Find the points of intersection of the circle with the segment AB.

## Solution

From the point A swing an arc of arbitrary radius intersecting the given circle. Let C and D be the points of intersection. Using Problem #7 bisect two arcs CD of the original circle.

### 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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