Circle Intersection Limit

Nick Chura
This is a problem from a calculus book. The circle with radius 1 and centered at (1, 0) is fixed. The circle centered at (0, 0) has variable radius r. The line through point (0, r) and the intersection point of the circles in the first quadrant is shown. This line has a positive horizontal intercept, shown as point E. What will happen to point E as the radius r decreases toward zero? Will it stay near its current location? Will it shoot off toward infinity? Will it diminish toward zero? 1. Make a guess. 2. Use the slider to change the value of r. 3. Could you have determined this result by using algebra and limits?