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5
2024 Geo Problem 5
2024 Geo Problem 5
Source:
April 15, 2024
geometry
Problem Statement
Triangle
A
B
C
ABC
A
BC
has
A
B
=
13
AB=13
A
B
=
13
,
B
C
=
14
BC=14
BC
=
14
, and
A
C
=
15
AC=15
A
C
=
15
. Let
P
P
P
lie on
B
C
‾
\overline{BC}
BC
, and let
D
D
D
and
E
E
E
be the feet of the perpendiculars from
P
P
P
onto
A
B
‾
\overline{AB}
A
B
and
A
C
‾
\overline{AC}
A
C
respectively. If
A
D
=
A
E
AD=AE
A
D
=
A
E
, find this common length.Proposed by Connor Gordon
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