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National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2017.8.4
2017.8.4
Part of
Kyiv City MO Juniors 2003+ geometry
Problems
(1)
collinear wanted, circle intersecting a square (2017 Kyiv City MO 8.4)
Source:
9/8/2020
On the sides
B
C
BC
BC
and
C
D
CD
C
D
of the square
A
B
C
D
ABCD
A
BC
D
, the points
M
M
M
and
N
N
N
are selected in such a way that
∠
M
A
N
=
4
5
o
\angle MAN= 45^o
∠
M
A
N
=
4
5
o
. Using the segment
M
N
MN
MN
, as the diameter, we constructed a circle
w
w
w
, which intersects the segments
A
M
AM
A
M
and
A
N
AN
A
N
at points
P
P
P
and
Q
Q
Q
, respectively. Prove that the points
B
,
P
B, P
B
,
P
and
Q
Q
Q
lie on the same line.
geometry
square
collinear