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2
SMT 2023 Geometry Tiebreaker #2
SMT 2023 Geometry Tiebreaker #2
Source:
August 9, 2023
geometry
Problem Statement
Triangle
△
A
B
C
\vartriangle ABC
△
A
BC
has side lengths
A
B
=
3
AB = 3
A
B
=
3
,
A
C
=
2
AC = 2
A
C
=
2
and angle
∠
C
B
A
=
3
0
o
\angle CBA = 30^o
∠
CB
A
=
3
0
o
. Let the possible lengths of
B
C
BC
BC
be
ℓ
1
\ell_1
ℓ
1
and
ℓ
2
\ell_2
ℓ
2
, where
ℓ
2
>
ℓ
1
\ell_2 > \ell_1
ℓ
2
>
ℓ
1
. Compute
ℓ
2
ℓ
1
\frac{\ell_2}{\ell_1}
ℓ
1
ℓ
2
.
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