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IMO Shortlist 2013, Geometry #2

Source: IMO Shortlist 2013, Geometry #2

July 9, 2014

geometrycircumcircletrapezoidsymmetryIMO Shortlist

Problem Statement

Let

\omega

be the circumcircle of a triangle

ABC

. Denote by

M

and

N

the midpoints of the sides

AB

and

AC

, respectively, and denote by

T

the midpoint of the arc

BC

of

Y

not containing

X

. The circumcircles of the triangles

Y

and

ANT

intersect the perpendicular bisectors of

AC

and

AB

at points

X

and

Y

, respectively; assume that

X

and

Y

lie inside the triangle

ABC

. The lines

MN

and

XY

intersect at

K

. Prove that

KA=KT

.

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