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2019 Junior Balkan MO, Problem 3

Source: 2019 Junior Balkan MO

June 22, 2019

geometryJBMOperpendicular bisectorcircumcirclegeometry solvedBalkanJunior Balkan

Problem Statement

Triangle

ABC

is such that

AB < AC

. The perpendicular bisector of side

BC

intersects lines

AB

and

AC

at points

P

and

Q

, respectively. Let

H

be the orthocentre of triangle

ABC

, and let

M

and

N

be the midpoints of segments

BC

and

PQ

, respectively. Prove that lines

HM

and

AN

meet on the circumcircle of

ABC

.

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