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2011 Princeton University Math Competition
A2 / B6
A2 / B6
Part of
2011 Princeton University Math Competition
Problems
(1)
2011 PUMaC Geometry A2 / B6
Source:
9/24/2019
A rectangular piece of paper has corners labeled
A
,
B
,
C
A, B, C
A
,
B
,
C
, and
D
D
D
, with
B
C
=
80
BC = 80
BC
=
80
and
C
D
=
120
CD = 120
C
D
=
120
. Let
M
M
M
be the midpoint of side
A
B
AB
A
B
. The corner labeled
A
A
A
is folded along line
M
D
MD
M
D
and the corner labeled
B
B
B
is folded along line
M
C
MC
MC
until the segments
A
M
AM
A
M
and
M
B
MB
MB
coincide. Let
S
S
S
denote the point in space where
A
A
A
and
B
B
B
meet. If
H
H
H
is the foot of the perpendicular from
S
S
S
to the original plane of the paper, find
H
M
HM
H
M
.
geometry