MathDB

Similar triangles involve centroid

Source: APMO 1991

March 11, 2006

trigonometrygeometry

Problem Statement

Let

G

be the centroid of a triangle

ABC

, and

M

be the midpoint of

BC

. Let

X

be on

AB

and

Y

on

AC

such that the points

X

,

Y

, and

GC

are collinear and

XY

and

BC

are parallel. Suppose that

ABC

and

GB

intersect at

Q

and

YB

and

GC

intersect at

P

. Show that triangle

MPQ

is similar to triangle

ABC

.

Back to Problems View on AoPS