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Contests
National and Regional Contests
Ecuador Contests
Ecuador Juniors
2019 Ecuador Juniors
3
3
Part of
2019 Ecuador Juniors
Problems
(1)
AE = CF iff BD bisects <ABC, 2 circumcircles 2019 Ecuador NMO (OMEC) 3.2
Source:
9/18/2021
Let
A
B
C
ABC
A
BC
be a triangle and
D
D
D
be a point on segment
A
C
AC
A
C
. The circumscribed circle of the triangle
B
D
C
BDC
B
D
C
cuts
A
B
AB
A
B
again at
E
E
E
and the circumference circle of the triangle
A
B
D
ABD
A
B
D
cuts
B
C
BC
BC
again at
F
F
F
. Prove that
A
E
=
C
F
AE = CF
A
E
=
CF
if and only if
B
D
BD
B
D
is the interior bisector of
∠
A
B
C
\angle ABC
∠
A
BC
.
geometry
circumcircle