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C O N S T R U C T I O N S
Constructing a circle through two points.Given two points A and B, construct a circle containing points A and B.
Step 1. Bisect line AB. Select any point P on this line, draw a circle with a radius of PA.
What if you were given three points? Given three non collinear points C,D, and E, construct a circle containing these three points.
Step 1. Bisect line CD and bisect line DE. These two lines intersect at K. Draw a circle at K with radius KC.
Constructing Tangencies.
Given a circle and a point on that circle, construct a line tangent to to the circle through that point.
Step 1. Draw a line from the center of the circle to the given point.
Step 2. Construct a line perpendicular to the line you just drew. It is tangent to the given circle. (Note: If there is a line tangent to a circle, note that if you connect the center of the circle to the point of tangency, that segment will be perpendicular to the tangent line.)
Constructing tangent arcs. Given an arc, construct another arc tangent to it.This is very easy.
Step 1. Draw a line from the center of the circle to the edge.
| Heptagon | Triangle and Hexagon | Pentagon | Golden Ratio | Nonagon |
| Pentadecagon | Heptadecagon | N-Gon | Squaring a Circle | Other Constructions |
