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Contests
National and Regional Contests
Bulgaria Contests
Bulgaria JBMO Team Selection Test
2014 Bulgaria JBMO TST
5
5
Part of
2014 Bulgaria JBMO TST
Problems
(1)
Geometry in a 45-60-75 triangle
Source:
5/18/2015
From the foot
D
D
D
of the height
C
D
CD
C
D
in the triangle
A
B
C
,
ABC,
A
BC
,
perpendiculars to
B
C
BC
BC
and
A
C
AC
A
C
are drawn, which they intersect at points
M
M
M
and
N
.
N.
N
.
Let
∠
C
A
B
=
6
0
∘
,
∠
C
B
A
=
4
5
∘
,
\angle CAB = 60^{\circ} , \angle CBA = 45^{\circ} ,
∠
C
A
B
=
6
0
∘
,
∠
CB
A
=
4
5
∘
,
and
H
H
H
be the orthocentre of
M
N
C
.
MNC.
MNC
.
If
O
O
O
is the midpoint of
C
D
,
CD,
C
D
,
find
∠
C
O
H
.
\angle COH.
∠
CO
H
.
geometry