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 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. 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 the problem was given in an earlier examination paper.
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.
Several proofs are known; one derives the theorem from the Japanese theorem for cyclic quadrilaterals.