MathDB

Given a scalene triangle

ABC

with circuncenter

O

and circumscribed circle

\Gamma

. Let

D, E ,F

the midpoints of

BC, AC, AB

. Let

M=OE \cap AD

N=OF \cap AD

and

P=CM \cap BN

. Let

X=AO \cap PE

Y=AP \cap OF

. Let

r

the tangent of

\Gamma

through

A

. Prove that

r, EF, XY

are concurrent.

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