MathDB

Let

ABC

be a triangle with circumcentre

O

. The points

D,E,F

lie in the interiors of the sides

BC,CA,AB

respectively, such that

DE

is perpendicular to

CO

and

DF

is perpendicular to

BO

. (By interior we mean, for example, that the point

D

lies on the line

BC

and

D

is between

B

and

C

on that line.) Let

K

be the circumcentre of triangle

AFE

. Prove that the lines

DK

and

BC

are perpendicular.
Netherlands (Merlijn Staps)

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