MathDB

Acute angle triangle is given such that

BC

is the longest side. Let

E

and

G

be the intersection points from the altitude from

A

BC

with the circumscribed circle of triangle

ABC

and

BC

respectively. Let the center

O

of this circle is positioned on the perpendicular line from

A

BE

. Let

EM

be perpendicular to

AC

and

EF

be perpendicular to

AB

. Prove that the area of

FBEG

is greater than the area of

MFE

Problem Statement