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LMT
2020 LMT Spring
30
30
Part of
2020 LMT Spring
Problems
(1)
Spring 2020 Team Round Problem 30
Source:
8/22/2020
Let
A
B
C
D
ABCD
A
BC
D
be a cyclic quadrilateral such that the ratio of its diagonals is
A
C
:
B
D
=
7
:
5.
AC:BD=7:5.
A
C
:
B
D
=
7
:
5.
Let
E
E
E
and
F
F
F
be the intersections of lines
A
B
AB
A
B
and
C
D
CD
C
D
and lines
B
C
BC
BC
and
A
D
AD
A
D
, respectively. Let
L
L
L
and
M
M
M
be the midpoints of diagonals
A
C
AC
A
C
and
B
D
BD
B
D
, respectively. Given that
E
F
=
2020
,
EF=2020,
EF
=
2020
,
the length of
L
M
LM
L
M
can be written as
p
q
\frac{p}{q}
q
p
where
p
,
q
p,q
p
,
q
are relatively prime positive integers. Compute
p
+
q
.
p+q.
p
+
q
.