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Geometry Indonesia Regional

Source: 2024 Indonesia Regional MO Essay Problem 3

May 6, 2024

geometryIndonesiaRMO

Problem Statement

Given a triangle

ABC

, points

X,Y,

and

Z

are the midpoints of

BC,CA,

and

AB

respectively. The perpendicular bisector of

AB

intersects line

XY

and line

AC

at

Z_1

and

Z_2

respectively. The perpendicular bisector of

AC

intersects line

XZ

and line

AB

at

Y_1

and

Y_2

respectively. Let

K

be a point such that

KZ_1 = KZ_2

and

KY_1 = KY_2

. Prove that

KB=KC

.

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