We begin by creating a point P, which is attached to a slider [i]a[/i].
Notice that point P is defined at (2;[i]a[/i]). What does the 2 represent in the point P? What does the [i]a[/i] represent?
The 2 represents the radius of the circle P is moving along. The [i]a[/i] represents the angle.
Now, we create a circle using [b]C=Circle[P,2][/b].
What can we say about this circle?
It is centered at point P and has a radius of 2. As [i]a[/i] slides, the circle moves in a circle.
We will now create a line segment [b]F=segment((4,0),(-4,0))[/b] to intersect our circle.
In how many places does the line segment intersect the circle?
We can create points where the line and the circle intersect.[br][list][*][b]A=Intersect(C,F,1)[/b][/*][*][b]B=Intersect(C,F,2)[/b][/*][/list]
As the center of the circle changes (by sliding [i]a[/i]), what do you notice about the intersection points?
One is moving and one is staying at the origin.
Make a conjecture about how you know which intersection point is moving and which remains at the origin.
Now, let's test your conjecture by creating a different line segment and its intersection points with the circle.
Does your conjecture change?