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Indonesia Regional
Indonesia Regional MO OSP SMA - geometry
2014.4
2014.4
Part of
Indonesia Regional MO OSP SMA - geometry
Problems
(1)
AN x AE = AD x AF = AB x AC , 2 circles related
Source: 2014 Indonesia MO Province P2 q4 OSP
12/10/2020
Let
Γ
\Gamma
Γ
be the circumcircle of triangle
A
B
C
ABC
A
BC
. One circle
ω
\omega
ω
is tangent to
Γ
\Gamma
Γ
at
A
A
A
and tangent to
B
C
BC
BC
at
N
N
N
. Suppose that the extension of
A
N
AN
A
N
crosses
Γ
\Gamma
Γ
again at
E
E
E
. Let
A
D
AD
A
D
and
A
F
AF
A
F
be respectively the line of altitude
A
B
C
ABC
A
BC
and diameter of
Γ
\Gamma
Γ
, show that
A
N
×
A
E
=
A
D
×
A
F
=
A
B
×
A
C
AN \times AE = AD \times AF = AB \times AC
A
N
×
A
E
=
A
D
×
A
F
=
A
B
×
A
C
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