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nice geometry

Source: 2021 Korea Winter Program Practice Test

February 8, 2021

geometryperpendicular bisectorcircumcircle

Problem Statement

E,F

are points on

AB,AC

that satisfies

(B,E,F,C)

cyclic.

D

is the intersection of

BC

and the perpendicular bisecter of

EF

, and

B',C'

are the reflections of

B,C

on

\triangle{CFB'}

.

X

is a point on the circumcircle of

\triangle{BEC'}

that

AB

is perpendicular to

BX

,and

Y

is a point on the circumcircle of

\triangle{CFB'}

that

AC

is perpendicular to

CY

. Show that

DX=DY

.

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