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2011 Cono Sur Olympiad
5
Cono Sur Olympiad 2011, Problem 5
Cono Sur Olympiad 2011, Problem 5
Source:
August 23, 2014
geometry
similar triangles
geometry proposed
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle and
D
D
D
a point in
A
C
AC
A
C
. If
∠
C
B
D
−
∠
A
B
D
=
6
0
∘
,
B
D
C
^
=
3
0
∘
\angle{CBD} - \angle{ABD} = 60^{\circ}, \hat{BDC} = 30^{\circ}
∠
CB
D
−
∠
A
B
D
=
6
0
∘
,
B
D
C
^
=
3
0
∘
and also
A
B
⋅
B
C
=
B
D
2
AB \cdot BC = BD^{2}
A
B
⋅
BC
=
B
D
2
, determine the measure of all the angles of triangle
A
B
C
ABC
A
BC
.
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