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Baltic Way
2001 Baltic Way
10
10
Part of
2001 Baltic Way
Problems
(1)
Determine the angles of ABC
Source: Baltic Way 2001
11/17/2010
In a triangle
A
B
C
ABC
A
BC
, the bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
meets the side
B
C
BC
BC
at the point
D
D
D
. Knowing that
∣
B
D
∣
⋅
∣
C
D
∣
=
∣
A
D
∣
2
|BD|\cdot |CD|=|AD|^2
∣
B
D
∣
⋅
∣
C
D
∣
=
∣
A
D
∣
2
and
∠
A
D
B
=
4
5
∘
\angle ADB=45^{\circ}
∠
A
D
B
=
4
5
∘
, determine the angles of triangle
A
B
C
ABC
A
BC
.
geometry
circumcircle
geometry proposed