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line perpendicular to the median of a triangle

Source: Sharygin Geometry Olympiad 2015 Final 8.6

August 1, 2018

geometryperpendicular bisectorperpendiculargeometry solvedSharygin Geometry OlympiadRussiamedian

Problem Statement

Lines

b

and

c

passing through vertices

B

and

C

of triangle

ABC

are perpendicular to sideline

BC

. The perpendicular bisectors to

AC

and

AB

meet

b

and

c

at points

P

and

Q

respectively. Prove that line

PQ

is perpendicular to median

AM

of triangle

ABC

.
(D. Prokopenko)