MathDB

2022 Team 5

Source:

March 14, 2022

geometrybarycentermidpointparallel

Problem Statement

Let

ABC

be a triangle with centroid

G

, and let

E

and

F

be points on side

BC

such that

BE = EF = F C

. Points

X

and

Y

lie on lines

AB

and

AC

, respectively, so that

X

,

Y

, and

G

are not collinear. If the line through

E

parallel to

XG

and the line through

F

parallel to

Y G

intersect at

P\ne G

, prove that

GP

passes through the midpoint of

XY

.

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