MathDB

2019 Central American and Caribbean Mathematical Olympiad, P3

Source:

June 18, 2019

geometrycircumcircle

Problem Statement

Let

ABC

be a triangle and

\Gamma

its circumcircle. Let

D

be the foot of the altitude from

A

to the side

BC

,

M

and

N

the midpoints of

EM

and

AC

, and

Q

the point on

\Gamma

diametrically opposite to

A

. Let

E

be the midpoint of

DQ

. Show that the lines perpendicular to

EM

and

EN

passing through

M

and

N

, respectively, meet on

AD

.

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