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Show that the circumcenter of triangle MDN lies on the line BC

Source: Moldova TST 2021

September 19, 2021

geometrycircumcircle

Problem Statement

Acute triangle

(AB)

with

AB>BC

is inscribed in circle

\Omega

. Points

D

and

E

, that lie on

(BC)

and

(AB)

are the feet of altitudes from

A

and

C

in triangle

ABC

, and

M

is the midpoint of the segment

DE

. Half-line

(AM

intersects the circle

\Omega

for the second time in

N

. Show that the circumcenter of triangle

MDN

lies on the line

BC

.

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