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IberoAmerican
2018 lberoAmerican
2
2
Part of
2018 lberoAmerican
Problems
(1)
Equal lengths in isosceles configuration
Source: Iberoamerican 2018 Problem 2
9/26/2018
Let
A
B
C
ABC
A
BC
be a triangle such that
∠
B
A
C
=
9
0
∘
\angle BAC = 90^{\circ}
∠
B
A
C
=
9
0
∘
and
A
B
=
A
C
AB = AC
A
B
=
A
C
. Let
M
M
M
be the midpoint of
B
C
BC
BC
. A point
D
≠
A
D \neq A
D
=
A
is chosen on the semicircle with diameter
B
C
BC
BC
that contains
A
A
A
. The circumcircle of triangle
D
A
M
DAM
D
A
M
cuts lines
D
B
DB
D
B
and
D
C
DC
D
C
at
E
E
E
and
F
F
F
respectively. Show that
B
E
=
C
F
BE = CF
BE
=
CF
.
geometry
circumcircle