# Two Circles and a Limit

Proof #3 by Mariano Perez de la Cruz

We are solving the Two Circles and a Limit problem:

A stationary circle of radius 3 is centered at

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Let F be the midpoint of AB, D the intersection of OF with the stationary circle in the upper half-plane, C the rightmost point of the stationary circle.

D is the circumcenter of the isosceles ΔAOB. This is because angles BOD and BCD are inscribed angles subtended by the same arc, whereas

ΔODC is right as is the angle OFE. Therefore, EA||CD. With the previous observation, the ratio EF/CD will tend to 2, while CD will approach OC. EF will then tend to twice the segment OC.

### Limits in Geometry

- Two Circles and a Limit
- A Geometric Limit
- Iterations in Geometry, an example
- Iterated Function Systems

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