Menelaus's theorem

If a line meets the sides

BC, CA

and

AB

of a triangle in points

P, Q

and

R

then the product of the ratios

\Large \frac {BP}{PC}.\frac {CQ}{QA}.\frac {AR}{RB}

is -1

Conversely, if points

P, Q

and

R

are on the three sides of the triangle and this ratio is -1 then the three points are collinear.