Chapter 10.7, Problem 1WE

a.

To determine

To place: The points $A$ and $B$ outside the circle $O$ , such that two points are on the circle.

Explanation of Solution

Given:

Two points $A$ and $B$ outside circle $O$ .

Concept used:

Circles and locus.

Calculation:

  

A line segment is drawn intersecting at two points.

In this, the numbers of points are two.

Conclusion:

Therefore, the numbers of points are two.

b.

To determine

To place: The points $A$ and $B$ outside the circle $O$ , such that no point is on the circle.

Explanation of Solution

Given:

Two points $A$ and $B$ outside circle $O$ .

Concept used:

Circles and locus.

Calculation:

  

The line segment is drawn such that it does not intersect the circle.

Conclusion:

Therefore, the numbers of points on the circle are zero.

c.

To determine

To place the points $A$ and $B$ outside the circle $O$ .

Explanation of Solution

Given:

Two points $A$ and $B$ outside circle $O$ , such that one point is on the circle.

Concept used:

Circles and locus.

Calculation:

This case will be a tangent to the circle $O$ .

  

Conclusion:

Therefore, there is only one intersecting point on the circle.