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2007 Cuba MO
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9
Part of
2007 Cuba MO
Problems
(1)
Cuba National MO
Source: Cuba Mathematical Olympiad 2007, grade 12, problem 3
1/26/2014
Let
O
O
O
be the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
, with
A
C
=
B
C
AC=BC
A
C
=
BC
end let
D
=
A
O
∩
B
C
D=AO\cap BC
D
=
A
O
∩
BC
. If
B
D
BD
B
D
and
C
D
CD
C
D
are integer numbers and
A
O
−
C
D
AO-CD
A
O
−
C
D
is prime, determine such three numbers.
geometry
circumcircle
inequalities
triangle inequality
geometry proposed