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line connecting centers of triangles DEN, DFM is perpendicular to AD

Source: Mathematics Regional Olympiad of Mexico Center Zone 2015 P5

November 12, 2021

geometryperpendicular

Problem Statement

In the triangle

ABC

, we have that

M

and

N

are points on

AB

and

AC

, respectively, such that

BC

is parallel to

MN

. A point

D

is chosen inside the triangle

AMN

. Let

E

and

F

be the points of intersection of

MN

with

BD

and

CD

, respectively. Show that the line joining the centers of the circles circumscribed to the triangles

DEN

and

DFM

is perpendicular to

AD