Menelaus's theorem

If a line meets the sides BC,CABC, CA and ABAB of a triangle in points P,QP, Q and RR then the product of the ratios

BPPC.CQQA.ARRB\Large \frac {BP}{PC}.\frac {CQ}{QA}.\frac {AR}{RB} is -1

Conversely, if points P,QP, Q and RR are on the three sides of the triangle and this ratio is -1 then the three points are collinear.