GeoGebra Classroom

# Warm-up: Chords and Secants

## 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 Quite lovely, after all.

## Figure 1: The Bare Necessities

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

Select all that apply
• A
• B
• C
• D
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?

1. The red line segment is longer than the blue line segment.
2. The green line segment is longer than the pink line segment.
3. The red and blue line segments overlap.
4. The green and pink line segments overlap.
How did you do this?

## 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?