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International Contests
International Olympiad of Metropolises
2018 IOM
2
2
Part of
2018 IOM
Problems
(1)
Quadratic concurrence in circumscribed quad
Source: IOM 2018 #2, Géza Kós
9/6/2018
A convex quadrilateral
A
B
C
D
ABCD
A
BC
D
is circumscribed about a circle
ω
\omega
ω
. Let
P
Q
PQ
PQ
be the diameter of
ω
\omega
ω
perpendicular to
A
C
AC
A
C
. Suppose lines
B
P
BP
BP
and
D
Q
DQ
D
Q
intersect at point
X
X
X
, and lines
B
Q
BQ
BQ
and
D
P
DP
D
P
intersect at point
Y
Y
Y
. Show that the points
X
X
X
and
Y
Y
Y
lie on the line
A
C
AC
A
C
.Géza Kós
geometry
IOM