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National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2013 India PRMO
9
9
Part of
2013 India PRMO
Problems
(1)
2013 preRMO p9, orthocenter, incentre, circumcentre, 1 vetrex concyclic
Source:
8/8/2019
In a triangle
A
B
C
ABC
A
BC
, let
H
,
I
H, I
H
,
I
and
O
O
O
be the orthocentre, incentre and circumcentre, respectively. If the points
B
,
H
,
I
,
C
B, H, I, C
B
,
H
,
I
,
C
lie on a circle, what is the magnitude of
∠
B
O
C
\angle BOC
∠
BOC
in degrees?
geometry
incenter
circumcircle
angle