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6
BMT 2022 Geometry #6 / General #24
BMT 2022 Geometry #6 / General #24
Source:
August 12, 2023
geometry
Problem Statement
Triangle
△
B
M
T
\vartriangle BMT
△
BMT
has
B
M
=
4
BM = 4
BM
=
4
,
B
T
=
6
BT = 6
BT
=
6
, and
M
T
=
8
MT = 8
MT
=
8
. Point
A
A
A
lies on line
B
M
↔
\overleftrightarrow{BM}
BM
and point
Y
Y
Y
lies on line
B
T
↔
\overleftrightarrow{BT}
BT
such that
A
Y
‾
\overline{AY}
A
Y
is parallel to
M
T
‾
\overline{MT}
MT
and the center of the circle inscribed in triangle
△
B
A
Y
\vartriangle BAY
△
B
A
Y
lies on
M
T
‾
\overline{MT}
MT
. Compute
A
Y
AY
A
Y
.
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