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Poland Contests
Poland - Second Round
2016 Poland - Second Round
5
5
Part of
2016 Poland - Second Round
Problems
(1)
Show that middle point of line segment lies on line
Source: 67 Polish MO 2016 Second Round - Problem 5
4/30/2018
Quadrilateral
A
B
C
D
ABCD
A
BC
D
is inscribed in circle. Points
P
P
P
and
Q
Q
Q
lie respectively on rays
A
B
→
AB^{\rightarrow}
A
B
→
and
A
D
→
AD^{\rightarrow}
A
D
→
such that
A
P
=
C
D
AP = CD
A
P
=
C
D
,
A
Q
=
B
C
AQ = BC
A
Q
=
BC
. Show that middle point of line segment
P
Q
PQ
PQ
lies on the line
A
C
AC
A
C
.
geometry
circle
Poland
quadrilateral
cyclic quadrilateral