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Problems
Contests
National and Regional Contests
Moldova Contests
Moldova Team Selection Test
1996 Moldova Team Selection Test
2
2
Part of
1996 Moldova Team Selection Test
Problems
(1)
Prove that $\angle AMC=\angle BND$ and $\angle ANC=\angle BMD$
Source: Moldova TST 1996
8/8/2023
Circles
S
1
S_1{}
S
1
and
S
2
S_2{}
S
2
intersect in
M
M{}
M
and
N
N{}
N
. Line
l
l
l
intersects the circles in points
A
,
B
∈
S
1
A,B\in S_1
A
,
B
∈
S
1
and
C
,
D
∈
S
2
C,D\in S_2
C
,
D
∈
S
2
. Prove that
∠
A
M
C
=
∠
B
N
D
\angle AMC=\angle BND
∠
A
MC
=
∠
BN
D
and
∠
A
N
C
=
∠
B
M
D
\angle ANC=\angle BMD
∠
A
NC
=
∠
BM
D
if the order of points on line
l
l
l
is: a) A,C,B,D; b)
A
,
C
,
D
,
B
.
A,C,D,B.
A
,
C
,
D
,
B
.
geometry