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Balkan MO Shortlist
2014 Balkan MO Shortlist
G3
G3
Part of
2014 Balkan MO Shortlist
Problems
(1)
Isosceles triangle
Source: Balkan MO 2014 G-3
6/10/2015
Let
△
A
B
C
\triangle ABC
△
A
BC
be an isosceles.
(
A
B
=
A
C
)
(AB=AC)
(
A
B
=
A
C
)
.Let
D
D
D
and
E
E
E
be two points on the side
B
C
BC
BC
such that
D
∈
B
E
D\in BE
D
∈
BE
,
E
∈
D
C
E\in DC
E
∈
D
C
and
2
∠
D
A
E
=
∠
B
A
C
2\angle DAE = \angle BAC
2∠
D
A
E
=
∠
B
A
C
.Prove that we can construct a triangle
X
Y
Z
XYZ
X
Y
Z
such that
X
Y
=
B
D
XY=BD
X
Y
=
B
D
,
Y
Z
=
D
E
YZ=DE
Y
Z
=
D
E
and
Z
X
=
E
C
ZX=EC
ZX
=
EC
.Find
∠
B
A
C
+
∠
Y
X
Z
\angle BAC + \angle YXZ
∠
B
A
C
+
∠
Y
XZ
.
geometry