User:Pro math user/sandbox

Kashanova's theorem is one of the most commonly used theorem by participants of IMO.￼

Definition: Let A be a collection of lines, that intersect with a given collection of circles, then |A| = ||R| • |K||, where R is a collection of lines that don't intersect with this given collection of circles and are not parallel, and where K is Kashanova's constant.

Proof: The proof of Kashanova's theorem is a particular case of Ram's theorem, where r = 1 and a = 0.