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National and Regional Contests
Russia Contests
All-Russian Olympiad
1990 All Soviet Union Mathematical Olympiad
521
521
Part of
1990 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 521 All Soviet Union MO 1990 concurrent circumcircles
Source:
8/14/2019
A
B
C
D
ABCD
A
BC
D
is a convex quadrilateral.
X
X
X
is a point on the side
A
B
.
A
C
AB. AC
A
B
.
A
C
and
D
X
DX
D
X
intersect at
Y
Y
Y
. Show that the circumcircles of
A
B
C
,
C
D
Y
ABC, CDY
A
BC
,
C
D
Y
and
B
D
X
BDX
B
D
X
have a common point.
circumcircle
concurrent
geometry