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perpendicular bisectors of PQ bisects two segments AO, BC, altitudes

Source: 2021 Saudi Arabia Training Lists p3 https://artofproblemsolving.com/community/c2758131_2021_saudi_arabia_training_tests

January 4, 2022

geometrybisects segmentperpendicular bisector

Problem Statement

Let

ABC

be an acute, non-isosceles triangle inscribed in (O) and

BB'

CC'

are altitudes. Denote

E, F

as the intersections of

BB'

CC'

with

(O)

and

D, P, Q

are projections of

A

BC

CE

BF

. Prove that the perpendicular bisectors of

PQ

bisects two segments

AO

BC