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2016 ASDAN Math Tournament
11
2016 Team #11
2016 Team #11
Source:
August 17, 2022
2016
team test
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
=
2
AB=2
A
B
=
2
,
B
C
=
3
BC=3
BC
=
3
, and
A
C
=
4
AC=4
A
C
=
4
. Consider all lines
X
Y
XY
X
Y
such that
X
X
X
lies on
A
C
AC
A
C
,
Y
Y
Y
lies on
B
C
BC
BC
, and
△
X
Y
C
\triangle XYC
△
X
Y
C
has area equal to half that of
△
A
B
C
\triangle ABC
△
A
BC
. What is the minimum possible length of
X
Y
XY
X
Y
?
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