MathDB

ASU 287 All Soviet Union MO 1980 |AM| + |AP| = a, area of ABCD < a^2 /2

Source:

July 19, 2019

geometryareasLocusmidpointsconvex

Problem Statement

The points

M

and

P

are the midpoints of

[BC]

and

[CD]

sides of a convex quadrangle

ABCD

. It is known that

|AM| + |AP| = a

. Prove that

ABCD

has area less than

\frac{a^2}{2}