MathDB

A convex quadrilateral

A B C D

with area of

S

is given. Inside each side of the quadrilateral a point is selected. These points are consecutively linked by segments, so that

A B C D

is split into a smaller quadrilateral and 4 triangles. Prove that the area of at least one triangle does not exceed

S / 8

. Mikhail Malkin

Problem Statement