MathDB

Let

ABC

be an acute triangle with

\angle ABC=60^{\circ}.

Suppose points

D

and

E

are on lines

AB

and

CB,

respectively, such that

CDB

and

AEB

are equilateral triangles. Given that the positive difference between the perimeters of

CDB

and

AEB

60

and

DE=45,

what is the value of

AB \cdot BC?

Proposed by Kyle Lee

Problem Statement