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Problems
Contests
National and Regional Contests
Turkey Contests
Akdeniz University MO
1996 Akdeniz University MO
5
5
Part of
1996 Akdeniz University MO
Problems
(1)
geometry
Source:
1/30/2016
Two circles centered
O
1
,
O
2
O_1,O_2
O
1
,
O
2
intersects at two points
M
M
M
and
N
N
N
.
O
1
M
O_1M
O
1
M
line intersects with
O
1
O_1
O
1
centered circle and
O
2
O_2
O
2
centered circle at
A
1
A_1
A
1
and
A
2
A_2
A
2
,
O
2
M
O_2M
O
2
M
line intersects with
O
1
O_1
O
1
centered circle and
O
2
O_2
O
2
centered circle at
B
1
B_1
B
1
and
B
2
B_2
B
2
respectively. Let
K
K
K
is intersection point of the
A
1
B
1
A_1B_1
A
1
B
1
and
A
2
B
2
A_2B_2
A
2
B
2
. Prove that
N
,
M
,
K
N,M,K
N
,
M
,
K
collinear.
Plane Geometry
geometry