MathDB

Triangles with equal area

Source: Costa Rica National Olympiad, Final Round, Problem 1

October 14, 2011

geometrygeometry unsolved

Problem Statement

Consider points

D,E

and

F

on sides

BC,AC

and

AB

, respectively, of a triangle

ABC

, such that

AD, BE

and

CF

concurr at a point

G

. The parallel through

G

BC

cuts

DF

and

DE

H

and

I

, respectively. Show that triangles

AHG

and

AIG

have the same areas.