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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
2004 Moldova Team Selection Test
3
3
Part of
2004 Moldova Team Selection Test
Problems
(1)
The cricles $\Gamma_1$ and $\Gamma_2$ intersect in $M$ and $N$.
Source: Moldova TST 2004
3/8/2023
The cricles
Γ
1
\Gamma_1
Γ
1
and
Γ
2
\Gamma_2
Γ
2
intersect in
M
M
M
and
N
.
N.
N
.
A line that goes through
M
M
M
intersects the cricles
Γ
1
\Gamma_1
Γ
1
and
Γ
2
\Gamma_2
Γ
2
in
A
A
A
and
B
B
B
, such that
M
∈
(
A
B
)
M\in(AB)
M
∈
(
A
B
)
. The bisector of angle
A
M
N
AMN
A
MN
intersects the circle
Γ
1
\Gamma_1
Γ
1
in
D
,
D,
D
,
and the bisector of angle
B
M
N
BMN
BMN
intersects the circle
Γ
2
\Gamma_2
Γ
2
in
C
.
C.
C
.
Prove that the circle with diameter
C
D
CD
C
D
splits the segment
A
B
AB
A
B
in half.
geometry