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Kvant Problems
Kvant 2023
M2735
M2735
Part of
Kvant 2023
Problems
(1)
Easy geo with circle
Source: Kvant Magazine No. 2 2023 M2735
4/19/2023
Let
A
B
AB
A
B
be a diameter of the circle
Ω
\Omega
Ω
with center
O
O{}
O
. The points
C
,
D
,
X
C, D, X
C
,
D
,
X
and
Y
Y{}
Y
are chosen on
Ω
\Omega
Ω
so that the segments
C
X
CX
CX
and
D
X
DX
D
X
intersect the segment
A
B
AB
A
B
at points symmetric with respect to
O
O{}
O
, and
X
Y
∥
A
B
XY\parallel AB
X
Y
∥
A
B
. Let the lines
A
B
AB{}
A
B
and
C
D
CD{}
C
D
intersect at the point
E
E
E
. Prove that the tangent to
Ω
\Omega
Ω
through
Y
Y{}
Y
passes through
E
E{}
E
.
geometry
circles