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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
1999 All-Russian Olympiad Regional Round
9.2
9.2
Part of
1999 All-Russian Olympiad Regional Round
Problems
(1)
B, E, D, F concyclic if AB = AD, BE = EC - All-Russian MO 1999 Regional (R4) 9.2
Source:
9/25/2024
In triangle
A
B
C
ABC
A
BC
, on side
A
C
AC
A
C
there are points
D
D
D
and
E
E
E
, that
A
B
=
A
D
AB = AD
A
B
=
A
D
and
B
E
=
E
C
BE = EC
BE
=
EC
(
E
E
E
between
A
A
A
and
D
D
D
). Point
F
F
F
is midpoint of arc
B
C
BC
BC
of circumcircle of triangle
A
B
C
ABC
A
BC
. Prove that the points
B
,
E
,
D
,
F
B, E, D, F
B
,
E
,
D
,
F
lie on the same circle.
geometry
Concyclic