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Hungary-Israel Binational
2002 Hungary-Israel Binational
2
Find the angles of a triangle
Find the angles of a triangle
Source: 13-th Hungary-Israel Binational Mathematical Competition 2002
April 7, 2007
geometry proposed
geometry
Problem Statement
Points
A
1
,
B
1
,
C
1
A_{1}, B_{1}, C_{1}
A
1
,
B
1
,
C
1
are given inside an equilateral triangle
A
B
C
ABC
A
BC
such that
B
1
A
B
^
=
A
1
B
A
^
=
1
5
0
,
C
1
B
C
^
=
B
1
C
B
^
=
2
0
0
,
A
1
C
A
^
=
C
1
A
C
^
=
2
5
0
\widehat{B_{1}AB}= \widehat{A1BA}= 15^{0}, \widehat{C_{1}BC}= \widehat{B_{1}CB}= 20^{0}, \widehat{A_{1}CA}= \widehat{C_{1}AC}= 25^{0}
B
1
A
B
=
A
1
B
A
=
1
5
0
,
C
1
BC
=
B
1
CB
=
2
0
0
,
A
1
C
A
=
C
1
A
C
=
2
5
0
. Find the angles of triangle
A
1
B
1
C
1
A_{1}B_{1}C_{1}
A
1
B
1
C
1
.
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