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2006 South africa National Olympiad
4
Obtuse isosceles triangle
Obtuse isosceles triangle
Source: South African MO 2006 Q4
May 27, 2012
geometry unsolved
geometry
Problem Statement
In triangle
A
B
C
ABC
A
BC
,
A
B
=
A
C
AB=AC
A
B
=
A
C
and
B
A
^
C
=
10
0
ā
B\hat{A}C=100^\circ
B
A
^
C
=
10
0
ā
. Let
D
D
D
be on
A
C
AC
A
C
such that
A
B
^
D
=
C
B
^
D
A\hat{B}D=C\hat{B}D
A
B
^
D
=
C
B
^
D
. Prove that
A
D
+
D
B
=
B
C
AD+DB=BC
A
D
+
D
B
=
BC
.
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