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International Contests
Iranian Geometry Olympiad
2014 Iranian Geometry Olympiad (junior)
P4
P4
Part of
2014 Iranian Geometry Olympiad (junior)
Problems
(1)
equal angles when <C = <A + 90^o
Source: IGO 2014 Junior 4
7/22/2018
In a triangle ABC we have
∠
C
=
∠
A
+
9
0
o
\angle C = \angle A + 90^o
∠
C
=
∠
A
+
9
0
o
. The point
D
D
D
on the continuation of
B
C
BC
BC
is given such that
A
C
=
A
D
AC = AD
A
C
=
A
D
. A point
E
E
E
in the side of
B
C
BC
BC
in which
A
A
A
doesn’t lie is chosen such that
∠
E
B
C
=
∠
A
,
∠
E
D
C
=
1
2
∠
A
\angle EBC = \angle A, \angle EDC = \frac{1}{2} \angle A
∠
EBC
=
∠
A
,
∠
E
D
C
=
2
1
∠
A
. Prove that
∠
C
E
D
=
∠
A
B
C
\angle CED = \angle ABC
∠
CE
D
=
∠
A
BC
.by Morteza Saghafian
geometry
equal angles