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2
SMT 2018 Geometry #12 trapezoid
SMT 2018 Geometry #12 trapezoid
Source:
August 8, 2023
geometry
trapezoid
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
be a trapezoid with
A
B
AB
A
B
parallel to
C
D
CD
C
D
and perpendicular to
B
C
BC
BC
. Let
M
M
M
be a point on
B
C
BC
BC
such that
∠
A
M
B
=
∠
D
M
C
\angle AMB = \angle DMC
∠
A
MB
=
∠
D
MC
. If
A
B
=
3
AB = 3
A
B
=
3
,
B
C
=
24
BC = 24
BC
=
24
, and
C
D
=
4
CD = 4
C
D
=
4
, what is the value of
A
M
+
M
D
AM + MD
A
M
+
M
D
?
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