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Problems
Contests
International Contests
Baltic Way
2016 Baltic Way
20
20
Part of
2016 Baltic Way
Problems
(1)
Concurrency in a cyclic quadrilateral
Source: Baltic Way 2016, Problem 20
11/5/2016
Let
A
B
C
D
ABCD
A
BC
D
be a cyclic quadrilateral with
A
B
AB
A
B
and
C
D
CD
C
D
not parallel. Let
M
M
M
be the midpoint of
C
D
.
CD.
C
D
.
Let
P
P
P
be a point inside
A
B
C
D
ABCD
A
BC
D
such that
P
A
=
P
B
=
C
M
.
P A = P B = CM.
P
A
=
PB
=
CM
.
Prove that
A
B
,
C
D
AB, CD
A
B
,
C
D
and the perpendicular bisector of
M
P
MP
MP
are concurrent.
geometry
cyclic quadrilateral