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PQ bisects segment connecting midpoints of CB and AB

Source: Tournament of Towns, Junior A-Level , Fall 2019 p4

April 19, 2020

angle bisectorgeometrybisects segmentperpendicular

Problem Statement

Let

OP

and

OQ

be the perpendiculars from the circumcenter

O

of a triangle

ABC

to the internal and external bisectors of the angle

B

. Prove that the line

PQ

divides the segment connecting midpoints of

CB

and

AB

into two equal parts.
(Artemiy Sokolov)