Two Circles

The graph shows two circles:
(x-1)² + (y-1)² = 1 and (x-2)² + (y-2)² = 2
There are two points of intersection: A and B.

Use the slider, p, to change the second circle.
Make p smaller until the circles intersect at A = (1,2) and B = (2,1)
(1) What is the equation of the circle now?
(2) Show by substitution in the circles' equations that A and B actually lie on both circles.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Dave Mulkey, Created with GeoGebra