Ceva's theorem



If points P,QP, Q and RR are on the sides BC,CABC, CA and ABAB of a triangle then the lines AP,BQAP, BQ and CRCR are concurrent if and only if the product of the ratios

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