MathDB

The triangles

ABG

and

AEF

are in the same plane. Between them the following conditions hold: (a)

E

is the mid-point of

AB

; (b) points

A,G

and

F

are on the same line; (c) there is a point

C

at which

BG

and

EF

intersect; (d)

|CE|=1

and

|AC|=|AE|=|FG|

. Show that if

|AG|=x

, then

|AB|=x^3

Problem Statement