# Warm-up: Chords and Secants

- Author:
- bildergairn

## Let's Begin

Here in Figure 1, we have a circle and two lines. Nice.
Each line intersects the circle, and the lines also intersect each other. We'll call the point where they intersect

**Q**. It is**Q**uite lovely, after all.## Figure 1: The Bare Necessities

How many points are created where the lines intersect the circle?

For each of those points on the circle, I've colored the line segment that runs from

**Q**to that point. One pair is**red**and**blue**, the other pair is**green**and**pink**.## Challenge 1

See if you can get the **red** and **blue** line segments to overlap. How did you do this?

## Challenge 2

Can you achieve the following objectives, all at the same time?

- The
**red**line segment is longer than the**blue**line segment. - The
**green**line segment is longer than the**pink**line segment. - The
**red**and**blue**line segments overlap. - The
**green**and**pink**line segments overlap.

## Challenge 3

One more challenge before you move on to Figure 2. Can you arrange the figure so that there are **only 3 points of intersection**?
How did you do this?