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Problem
Problem
Show that the distance between the circumcentre and the orthocentre of a triangle
A
B
C
ABC
A
B
C
is
R
1
−
8
cos
A
cos
B
cos
C
R \sqrt{1 - 8 \cos A \cos B \cos C}
R
1
−
8
cos
A
cos
B
cos
C
.
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