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2020 LMT Spring
23
Spring 2020 Team Round Problem 23
Spring 2020 Team Round Problem 23
Source:
August 22, 2020
Problem Statement
Let
△
A
B
C
\triangle ABC
△
A
BC
be a triangle such that
A
B
=
A
C
=
40
AB=AC=40
A
B
=
A
C
=
40
and
B
C
=
79.
BC=79.
BC
=
79.
Let
X
X
X
and
Y
Y
Y
be the points on segments
A
B
AB
A
B
and
A
C
AC
A
C
such that
A
X
=
5
,
A
Y
=
25.
AX=5, AY=25.
A
X
=
5
,
A
Y
=
25.
Given that
P
P
P
is the intersection of lines
X
Y
XY
X
Y
and
B
C
,
BC,
BC
,
compute
P
X
⋅
P
Y
−
P
B
⋅
P
C
.
PX\cdot PY-PB\cdot PC.
PX
⋅
P
Y
−
PB
⋅
PC
.
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