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Kvant Problems
Kvant 2021
M2654
M2654
Part of
Kvant 2021
Problems
(1)
parallelogram given, tangency wanted
Source: All-Russian 2021/10.1
4/19/2021
On the side
B
C
BC
BC
of the parallelogram
A
B
C
D
ABCD
A
BC
D
, points
E
E
E
and
F
F
F
are given (
E
E
E
lies between
B
B
B
and
F
F
F
) and the diagonals
A
C
,
B
D
AC, BD
A
C
,
B
D
meet at
O
O
O
. If it's known that
A
E
,
D
F
AE, DF
A
E
,
D
F
are tangent to the circumcircle of
△
A
O
D
\triangle AOD
△
A
O
D
, prove that they're tangent to the circumcircle of
△
E
O
F
\triangle EOF
△
EOF
as well.
geometry
Angle Chasing