# Circle Intersection Limit

- Author:
- Nick Chura

- Topic:
- Circle, Intersection

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

**. 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***r**. What will happen to point***E***as the radius***E***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?***r**