MathDB

Let

ABC

be an equilateral triangle of unit side length and suppose

D

is a point on segment

\overline{BC}

such that

DB<DC.

Let

M

and

N

denote the midpoints of

\overline{AB}

and

\overline{AC},

respectively. Suppose

X

and

Y

are the intersections of lines

AB

and

ND,

and lines

AC

and

MD,

respectively. Given that

XY=4,

what is the value of

\frac{DB}{DC}?

Proposed by Kyle Lee

Problem Statement