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2024 JHMT HS
5
Cevian and Equal Perimeters
Cevian and Equal Perimeters
Source:
September 7, 2024
geometry
2024
Problem Statement
Triangle
J
H
U
JHU
J
H
U
has side lengths
J
H
=
13
JH=13
J
H
=
13
,
H
U
=
14
HU=14
H
U
=
14
, and
J
U
=
15
JU=15
J
U
=
15
. Point
X
X
X
lies on
H
U
‾
\overline{HU}
H
U
such that
△
J
H
X
\triangle{JHX}
△
J
H
X
and
△
J
U
X
\triangle{JUX}
△
J
U
X
have equal perimeters. Compute
J
X
2
JX^2
J
X
2
.
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