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Cono Sur Olympiad
2018 Cono Sur Olympiad
1
1
Part of
2018 Cono Sur Olympiad
Problems
(1)
First problem
Source: Cono sur 2018
8/26/2018
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral, where
R
R
R
and
S
S
S
are points in
D
C
DC
D
C
and
A
B
AB
A
B
, respectively, such that
A
D
=
R
C
AD=RC
A
D
=
RC
and
B
C
=
S
A
BC=SA
BC
=
S
A
. Let
P
P
P
,
Q
Q
Q
and
M
M
M
be the midpoints of
R
D
RD
R
D
,
B
S
BS
BS
and
C
A
CA
C
A
, respectively. If
∠
M
P
C
+
∠
M
Q
A
=
90
\angle MPC + \angle MQA = 90
∠
MPC
+
∠
MQ
A
=
90
, prove that
A
B
C
D
ABCD
A
BC
D
is cyclic.
geometry
cono sur