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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
1998 National Olympiad First Round
13
13
Part of
1998 National Olympiad First Round
Problems
(1)
Orthocenter
Source: 0
4/23/2009
Let
H
H
H
be the intersection of altitudes in triangle
A
B
C
ABC
A
BC
. If \angle B\equal{}\angle C\equal{}\alpha and
O
O
O
is the center of circle passing through
A
A
A
,
H
H
H
and
C
C
C
, then find
∠
H
O
C
\angle HOC
∠
H
OC
in terms of
α
\alpha
α
.
(A)
\ 90{}^\circ \minus{}\alpha \qquad
(B)
\ 90{}^\circ \plus{}\frac{\alpha }{2} \qquad
(C)
\ 180{}^\circ \minus{}\alpha \\ \qquad
(D)
\ 180{}^\circ \minus{}\frac{\alpha }{2} \qquad
(E)
\ 180{}^\circ \minus{}2\alpha
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