MathDB

Let

ABCD

be a cyclic quadrilateral such that the ratio of its diagonals is

AC:BD=7:5.

Let

E

and

F

be the intersections of lines

AB

and

CD

and lines

BC

and

AD

, respectively. Let

L

and

M

be the midpoints of diagonals

AC

and

BD

, respectively. Given that

EF=2020,

the length of

LM

can be written as

\frac{p}{q}

where

p,q

are relatively prime positive integers. Compute

p+q.

Problem Statement