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National and Regional Contests
Iran Contests
Iran MO (2nd Round)
2016 Iran MO (2nd Round)
5
Iran geometry
Iran geometry
Source: Iran second round 2016, day 2, problem 5
April 29, 2016
geometry
Problem Statement
A
B
C
D
ABCD
A
BC
D
is a quadrilateral such that
∠
A
C
B
=
∠
A
C
D
\angle ACB=\angle ACD
∠
A
CB
=
∠
A
C
D
.
T
T
T
is inside of
A
B
C
D
ABCD
A
BC
D
such that
∠
A
D
C
−
∠
A
T
B
=
∠
B
A
C
\angle ADC-\angle ATB=\angle BAC
∠
A
D
C
−
∠
A
TB
=
∠
B
A
C
and
∠
A
B
C
−
∠
A
T
D
=
∠
C
A
D
\angle ABC-\angle ATD=\angle CAD
∠
A
BC
−
∠
A
T
D
=
∠
C
A
D
. Prove that
∠
B
A
T
=
∠
D
A
C
\angle BAT=\angle DAC
∠
B
A
T
=
∠
D
A
C
.
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