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Lines contained in one point

Source: Brazil National Olympiad 2019 - level 2 - #3

November 23, 2019

euclidean geometrygeometryBrazilian Math Olympiad

Problem Statement

Let

ABC

be an acutangle triangle inscribed in a circle

P

of center

Q

. Let

EF

be the height of the vertex

A

. Let E and F be points over

\Gamma

such that

AE = AD = AF

. Let

P

and

Q

be the intersection points of the

EF

with sides

AB

and

AC

respectively. Let

X

be the second intersection point of

\Gamma

with the circle circumscribed to the triangle

AP Q

. Show that the lines

XD

and

AO

meet at a point above sobre

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