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Menelaus theorem

Source: Nigeria Olympiad senior mathematics round 2 2020 problem 2

January 19, 2020

geometry

Problem Statement

Let

D

be a point in the interior of

ABC

. Let

BD

and

AC

intersect at

E

while

CD

and

AB

intersect at

F

. Let

EF

intersect

BC

at

G

. Let

H

be an arbitrary point on

AD

. Let

HF

and

BD

intersect at

I

. Let

HE

and

CD

intersect at

J

. prove that

G

,

I

and

J

are collinear

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