MathDB

Math Prize 2011 Problem 9

Source:

September 19, 2011

analytic geometrygeometryratioAMCAIMEMath Prize for Girlsnumber theory

Problem Statement

Let

ABC

be a triangle. Let

D

be the midpoint of

\overline{BC}

, let

E

be the midpoint of

\overline{AD}

, and let

F

be the midpoint of

\overline{BE}

. Let

G

be the point where the lines

AB

and

CF

intersect. What is the value of

\frac{AG}{AB}