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National and Regional Contests
Poland Contests
Poland - Second Round
1969 Poland - Second Round
3
3
Part of
1969 Poland - Second Round
Problems
(1)
concyclic , given cyclic quad
Source: Polish MO second round 1969 p3
8/28/2024
Given a quadrilateral
A
B
C
D
ABCD
A
BC
D
inscribed in a circle. The images of the points
A
A
A
and
C
C
C
in symmetry with respect to the line
B
D
BD
B
D
are the points
A
′
A'
A
′
and
C
′
C'
C
′
, respectively, and the images of the points
B
B
B
and
D
D
D
in symmetry with respect to the line
A
C
AC
A
C
are the points
B
′
B'
B
′
and
D
′
D'
D
′
respectively. Prove that the points
A
′
A'
A
′
,
B
′
B'
B
′
,
C
′
C'
C
′
,
D
′
D'
D
′
lie on the circle.
geometry
Concyclic
Cyclic