MathDB

Bosnia 2009 Problem 5

Source:

August 8, 2010

geometrygeometry proposed

Problem Statement

Line

p

intersects sides

AB

and

BC

of triangle

\triangle ABC

at points

M

and

K.

If area of triangle

\triangle MBK

is equal to area of quadrilateral

AMKC,

prove that

\frac{\left|MB\right|+\left|BK\right|}{\left|AM\right|+\left|CA\right|+\left|KC\right|}\geq\frac{1}{3}