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Bulgarian Spring Mathematical Competition
2024 Bulgarian Spring Mathematical Competition
11.2
11.2
Part of
2024 Bulgarian Spring Mathematical Competition
Problems
(1)
Conditional geometry with parallelogram
Source: Bulgarian Spring Tournament 2024 11.2
3/31/2024
Let
A
B
C
D
ABCD
A
BC
D
be a parallelogram and a circle
k
k
k
passes through
A
,
C
A, C
A
,
C
and meets rays
A
B
,
A
D
AB, AD
A
B
,
A
D
at
E
,
F
E, F
E
,
F
. If
B
D
,
E
F
BD, EF
B
D
,
EF
and the tangent at
C
C
C
concur, show that
A
C
AC
A
C
is diameter of
k
k
k
.
geometry
parallelogram