MathDB

Moldova JTST 2019 P7

Source:

April 19, 2019

geometry

Problem Statement

Point

H

is the orthocenter of the acute triangle

\Delta ABC

and point

K

,situated on the line

(BC)

, is the foot of the perpendicular from point

A

.The circle

\Omega

passes through points

A

and

K

,intersecting the sides

(AB)

and

(AC)

in points

M

and

N

.The line that passes through point

A

and is parallel with

BC

intersects again the circumcircles of triangles

\Delta AHM

and

\Delta AHN

in points

X

and

Y

.Prove that

XY =BC

.

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