Answer Keys.

Colinear Points

THREE points are colinear, so all of them are on a line.

If three are colinear, there are three cases.

1. There are no points in common.
2. There are two points in common.
3. All of them are in common.

Number of Intersections

We know that the maximum number of intersections, that a circle and a line can have is two.

Definition of Circle

A circle is a FIGURE that the radius is equal.

Solution.

For cases 2 and 3, let's EXCLUDE them.

We know the maximum number of intersections is 2. Based on that, let's find the total number of ways.

• Location of the center?
• The pair of intersections?

There are three ways to choose the pair of points and two ways to choose a center. Total of 6 different circles.

Now there are two general cases.

• One point is outside the circle. (4 circles)
• One point is inside the circle. (2 circles)

In either WAY, the circles cannot go through one point because the distance is different from the two points.

More information.

If one point is outside the circle, the distance from the circle is greater than the radius.

If one point is inside the circle, the distance from the circle is less than the radius.