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IP _|_ BC if EP _|_ MAn and NP // IA

Source: Mathematics Regional Olympiad of Mexico Northeast 2018 P2

September 12, 2022

geometryperpendicularincenter

Problem Statement

Let

ABC

be a triangle such that

M

and

N

are the midpoints of

AC

and

BC

, respectively. Let

I

be the incenter of

ABC

and

E

be the intersection of

MN

with

Bl

. Let

P

be a point such that

EP

is perpendicular to

MN

and

NP

parallel to

IA

. Prove that

IP

is perpendicular to

BC