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2013 EGMO
1
1
Part of
2013 EGMO
Problems
(1)
AD=BE implies ABC right
Source: European Girl's MO 2013, Problem 1
4/10/2013
The side
B
C
BC
BC
of the triangle
A
B
C
ABC
A
BC
is extended beyond
C
C
C
to
D
D
D
so that
C
D
=
B
C
CD = BC
C
D
=
BC
. The side
C
A
CA
C
A
is extended beyond
A
A
A
to
E
E
E
so that
A
E
=
2
C
A
AE = 2CA
A
E
=
2
C
A
. Prove that, if
A
D
=
B
E
AD=BE
A
D
=
BE
, then the triangle
A
B
C
ABC
A
BC
is right-angled.
geometry
circumcircle
Triangle
EGMO
EGMO 2013