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Indonesia Regional Part II P5

Source: Indonesia Regional 2023, Part II P5

June 5, 2023

geometryIndonesiaregional olympiadRMO

Problem Statement

Given

\triangle ABC

and points

D

and

E

at the line

BC

, furthermore there are points

X

and

Y

inside

\triangle ABC

. Let

P

be the intersection of line

AD

and

XE

, and

Q

be the intersection of line

AE

and

YD

. If there exist a circle that passes through

X, Y, D, E

, and

\angle BXE + \angle BCA = \angle CYD + \angle CBA = 180^{\circ}

Prove that the line

BP

,

CQ

, and the perpendicular bisector of

BC

intersect at one point.

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