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IMO Shortlist 2012, Geometry 4

Source: IMO Shortlist 2012, Geometry 4

July 29, 2013

geometrycircumcircletrigonometryTriangleIMO Shortlist

Problem Statement

Let

ABC

be a triangle with

AB \neq AC

and circumcenter

O

. The bisector of

\angle BAC

intersects

BC

at

D

. Let

E

be the reflection of

D

with respect to the midpoint of

BC

. The lines through

D

and

E

perpendicular to

BC

intersect the lines

AO

and

AD

at

X

and

Y

respectively. Prove that the quadrilateral

BXCY

is cyclic.

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