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4
2016 Geo #4
2016 Geo #4
Source:
December 30, 2016
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
=
3
AB = 3
A
B
=
3
,
A
C
=
8
AC = 8
A
C
=
8
,
B
C
=
7
BC = 7
BC
=
7
and let
M
M
M
and
N
N
N
be the midpoints of
A
B
‾
\overline{AB}
A
B
and
A
C
‾
\overline{AC}
A
C
, respectively. Point
T
T
T
is selected on side
B
C
BC
BC
so that
A
T
=
T
C
AT = TC
A
T
=
TC
. The circumcircles of triangles
B
A
T
BAT
B
A
T
,
M
A
N
MAN
M
A
N
intersect at
D
D
D
. Compute
D
C
DC
D
C
.
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