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Argentina Contests
Argentina National Olympiad
2013 Argentina National Olympiad
2
2
Part of
2013 Argentina National Olympiad
Problems
(1)
computational, convex ABCD,<A=<C, B bisector passes midpoint of CD, CD=3AB
Source: 2013 Argentina OMA L3 p2
6/17/2020
In a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
the angles
∠
A
\angle A
∠
A
and
∠
C
\angle C
∠
C
are equal and the bisector of
∠
B
\angle B
∠
B
passes through the midpoint of the side
C
D
CD
C
D
. If it is known that
C
D
=
3
A
D
CD = 3AD
C
D
=
3
A
D
, calculate
A
B
B
C
\frac{AB}{BC}
BC
A
B
.
convex quadrilateral
equal angles
ratio
angle bisector
geometry