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Greece Junior Math Olympiad
2020 Greece Junior Math Olympiad
2
2
Part of
2020 Greece Junior Math Olympiad
Problems
(1)
angle chasing, in terms of angles (Greece junior 2019 p2)
Source:
2/23/2020
Let
A
B
C
ABC
A
BC
be an acute-angled triangle with
A
B
<
A
C
AB<AC
A
B
<
A
C
. Let
D
D
D
be the midpoint of side
B
C
BC
BC
and
B
E
,
C
Z
BE,CZ
BE
,
CZ
be the altitudes of the triangle
A
B
C
ABC
A
BC
. Line
Z
E
ZE
ZE
intersects line
B
C
BC
BC
at point
O
O
O
. (i) Find all the angles of the triangle
Z
D
E
ZDE
Z
D
E
in terms of angle
∠
A
\angle A
∠
A
of the triangle
A
B
C
ABC
A
BC
(ii) Find the angle
∠
B
O
Z
\angle BOZ
∠
BOZ
in terms of angles
∠
B
\angle B
∠
B
and
∠
C
\angle C
∠
C
of the triangle
A
B
C
ABC
A
BC
geometry
angles
altitudes