Eyeball_theorem
Eyeball theorem
Statement in elementary geometry
The eyeball theorem is a statement in elementary geometry about a property of a pair of disjoined circles.
More precisely it states the following:[1]
- For two nonintersecting circles and centered at and the tangents from P onto intersect at and and the tangents from Q onto intersect at and . Then .
The eyeball theorem was discovered in 1960 by the Peruvian mathematician Antonio Gutierrez.[2] However without the use of its current name it was already posed and solved as a problem in an article by G. W. Evans in 1938.[3] Furthermore Evans stated that problem was given in an earlier examination paper.[4]
A variant of this theorem states, that if one draws line in such a way that it intersects for the second time at and at . Then, it turns out that .[3]