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Mathematics
Mathematics
Problem
Let
A
B
C
ABC
A
B
C
be an acute triangle with circumcenter
O
O
O
, and let
K
K
K
be a point such that
K
A
KA
K
A
is tangent to circumcircle
(
A
B
C
)
(ABC)
(
A
B
C
)
and
∠
K
C
B
=
90
∘
\angle KCB = 90^\circ
∠
K
C
B
=
9
0
∘
. Let
A
O
AO
A
O
meet
B
C
BC
B
C
at
D
D
D
. Prove that
K
D
∥
A
B
KD \parallel AB
K
D
∥
A
B
.
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