Eyeball theorem

The eyeball theorem is a statement in elementary geometry about a property of a pair of disjoined circles.

More precisely it states the following:
 * ''For two nonintersecting circles $$c_P$$ and $$c_Q$$centered at $$P$$ and $$Q$$ the tangents from P onto $$c_Q$$ intersect $$c_Q$$ at $$C $$ and $$D$$ and the tangents from Q onto $$c_P$$ intersect $$c_P$$ at $$A $$ and $$B$$. Then $$|AB| = |CD|$$.

The eyeball theorem was discovered in 1960 by the Peruvian mathematician Antonio Gutierrez. 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. Furthermore Evans stated that problem was given in an earlier examination paper.

A variant of this theorem states, that if one draws line $$FJ$$ in such a way that it intersects $$c_P$$ for the second time at $$F'$$ and $$c_Q$$ at $$J'$$. Then, it turns out that $$|FF'|=|JJ'|$$.

There are some proofs for Eyeball theorem, one of them show that this theorem is a consequence of the Japanese theorem for cyclic quadrilaterals.