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Problems
Contests
National and Regional Contests
Switzerland Contests
Swiss NMO - geometry
2021.2
2021.2
Part of
Swiss NMO - geometry
Problems
(1)
Angle chasing problem
Source: Switzerland Final Round 2021 P2
2/24/2021
Let
△
A
B
C
\triangle ABC
△
A
BC
be an acute triangle with
A
B
=
A
C
AB =AC
A
B
=
A
C
and let
D
D
D
be a point on the side
B
C
BC
BC
. The circle with centre
D
D
D
passing through
C
C
C
intersects
⊙
(
A
B
D
)
\odot(ABD)
⊙
(
A
B
D
)
at points
P
P
P
and
Q
Q
Q
, where
Q
Q
Q
is the point closer to
B
B
B
. The line
B
Q
BQ
BQ
intersects
A
D
AD
A
D
and
A
C
AC
A
C
at points
X
X
X
and
Y
Y
Y
respectively. Prove that quadrilateral
P
D
X
Y
PDXY
P
D
X
Y
is cyclic.
geometry