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2019 Stanford Mathematics Tournament
10
10
Part of
2019 Stanford Mathematics Tournament
Problems
(1)
SMT 2019 Geometry #10
Source:
8/8/2023
Let
A
B
C
ABC
A
BC
be an acute triangle with
B
C
=
48
BC = 48
BC
=
48
. Let
M
M
M
be the midpoint of
B
C
BC
BC
, and let
D
D
D
and
E
E
E
be the feet of the altitudes drawn from
B
B
B
and
C
C
C
to
A
C
AC
A
C
and
A
B
AB
A
B
respectively. Let
P
P
P
be the intersection between the line through
A
A
A
parallel to
B
C
BC
BC
and line
D
E
DE
D
E
. If
A
P
=
10
AP = 10
A
P
=
10
, compute the length of
P
M
PM
PM
,
geometry