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4
2017 Geometry #4: Quadrilateral Finding MN^2-PQ^2
2017 Geometry #4: Quadrilateral Finding MN^2-PQ^2
Source:
February 19, 2017
geometry
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral with
A
B
=
5
AB=5
A
B
=
5
,
B
C
=
6
BC=6
BC
=
6
,
C
D
=
7
CD=7
C
D
=
7
, and
D
A
=
8
DA=8
D
A
=
8
. Let
M
M
M
,
P
P
P
,
N
N
N
,
Q
Q
Q
be the midpoints of sides
A
B
AB
A
B
,
B
C
BC
BC
,
C
D
CD
C
D
,
D
A
DA
D
A
respectively. Compute
M
N
2
ā
P
Q
2
MN^2-PQ^2
M
N
2
ā
P
Q
2
.
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