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4
SMT 2020 Geometry #4
SMT 2020 Geometry #4
Source:
August 9, 2023
geometry
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
be a quadrilateral such that
A
B
=
B
C
=
13
AB = BC = 13
A
B
=
BC
=
13
,
C
D
=
D
A
=
15
CD = DA = 15
C
D
=
D
A
=
15
and
A
C
=
24
AC = 24
A
C
=
24
. Let the midpoint of
A
C
AC
A
C
be
E
E
E
. What is the area of the quadrilateral formed by connecting the incenters of
A
B
E
ABE
A
BE
,
B
C
E
BCE
BCE
,
C
D
E
CDE
C
D
E
, and
D
A
E
DAE
D
A
E
?
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