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Intersection point of perpendicular bisectors satisfies property

Source: Mexico National Olympiad Mock Exam 2019 P6

October 16, 2019

geometrysymmedianCircumcenterperpendicular bisector

Problem Statement

Let

ABC

be a scalene triangle with circumcenter

O

, and let

D

and

E

be points inside angle

\measuredangle BAC

such that

A

lies on line

DE

, and

K

and

\angle AEC=\angle BCA

. Let

M

be the midpoint of

BC

and

K

be a point such that

OK

is perpendicular to

AO

and

\angle BAK=\angle MAC

. Finally, let

P

be the intersection of the perpendicular bisectors of

BD

and

CE

. Show that

KO=KP

.
Proposed by Victor Domínguez

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