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Mediterranean Mathematics Olympiad
2007 Mediterranean Mathematics Olympiad
3
3
Part of
2007 Mediterranean Mathematics Olympiad
Problems
(1)
Compute all possible lengths of sides AB and AC
Source: Mediterranean MO 2007
10/31/2010
In the triangle
A
B
C
ABC
A
BC
, the angle
α
=
∠
B
A
C
\alpha = \angle BAC
α
=
∠
B
A
C
and the side
a
=
B
C
a = BC
a
=
BC
are given. Assume that
a
=
r
R
a = \sqrt{rR}
a
=
r
R
, where
r
r
r
is the inradius and
R
R
R
the circumradius. Compute all possible lengths of sides
A
B
AB
A
B
and
A
C
.
AC.
A
C
.
geometry
inradius
trigonometry
quadratics
geometry unsolved