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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2011 All-Russian Olympiad Regional Round
9.2
9.2
Part of
2011 All-Russian Olympiad Regional Round
Problems
(1)
A problem about isosceles triangle and related circumcirles
Source:
9/1/2011
Consider an isosceles triangle
A
B
C
ABC
A
BC
with
A
B
=
A
C
AB=AC
A
B
=
A
C
. Point
D
D
D
is on the smaller arc
A
B
AB
A
B
of its circumcirle. Point
E
E
E
lies on the continuation of segment
A
D
AD
A
D
beyond point
D
D
D
so that both
A
A
A
and
E
E
E
lie in the same half-plane relative to
B
C
BC
BC
. The circumcirle of triangle
B
D
E
BDE
B
D
E
intersects side
A
B
AB
A
B
at point
F
F
F
. Prove that lines
E
F
EF
EF
and
B
C
BC
BC
are parallel. (Author: R. Zhenodarov)
geometry
circumcircle