MathDB

Lots of Equilateral Triangles

Source: 2015 AIME I Problem 4

March 20, 2015

AMCAIMEAIME ISpiral Similaritygeometrygeometry solved2015 AIME I

Problem Statement

Point

B

lies on line segment

\overline{AC}

with

AB=16

and

BC=4

. Points

D

and

E

lie on the same side of line

AC

forming equilateral triangles

\triangle ABD

and

\triangle BCE

. Let

M

be the midpoint of

\overline{AE}

, and

N

be the midpoint of

\overline{CD}

. The area of

\triangle BMN

is

x

. Find

x^2

.

Back to Problems View on AoPS