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International Contests
IMO Longlists
1977 IMO Longlists
30
30
Part of
1977 IMO Longlists
Problems
(1)
Prove that BS = BC (chosing the angles) - [ILL 1977]
Source:
1/11/2011
A triangle
A
B
C
ABC
A
BC
with
∠
A
=
3
0
∘
\angle A = 30^\circ
∠
A
=
3
0
∘
and
∠
C
=
5
4
∘
\angle C = 54^\circ
∠
C
=
5
4
∘
is given. On
B
C
BC
BC
a point
D
D
D
is chosen such that
∠
C
A
D
=
1
2
∘
.
\angle CAD = 12^\circ.
∠
C
A
D
=
1
2
∘
.
On
A
B
AB
A
B
a point
E
E
E
is chosen such that
∠
A
C
E
=
6
∘
.
\angle ACE = 6^\circ.
∠
A
CE
=
6
∘
.
Let
S
S
S
be the point of intersection of
A
D
AD
A
D
and
C
E
.
CE.
CE
.
Prove that
B
S
=
B
C
.
BS = BC.
BS
=
BC
.
geometry unsolved
geometry