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RMT 2015 Geometry #8
RMT 2015 Geometry #8
Source:
October 28, 2022
geometry
Problem Statement
Consider the parallelogram
A
B
C
D
ABCD
A
BC
D
such that
C
D
=
8
CD = 8
C
D
=
8
and
B
C
=
14
BC = 14
BC
=
14
. The diagonals
A
C
‾
\overline{AC}
A
C
and
B
D
‾
\overline{BD}
B
D
intersect at
E
E
E
and
A
C
=
16
AC = 16
A
C
=
16
. Consider a point
F
F
F
on the segment
E
D
‾
\overline{ED}
E
D
with
F
D
=
66
3
F D =\frac{\sqrt{66}}{3}
F
D
=
3
66
. Compute
C
F
CF
CF
.
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