# 2016 AMC 12A Problems/Problem 12

Revision as of 12:59, 4 February 2016 by Warrenwangtennis (talk | contribs) (Created page with "== Solution == By the angle bisector theorem, <math>\frac{AB}{AE} = \frac{CB}{CE}</math> <math>\frac{6}{AE} = \frac{7}{8 - AE}</math>, so <math>AE = \frac{48}{13}</math> Sim...")

## Solution

By the angle bisector theorem,

, so

Similarly,

Now, we use mass points.

Assign point a mass of .

Because will have a mass of .

Similarly, will have a mass of .

.

Similarly, .

The mass of is the sum of the masses of and .

.

This can be checked with , which is also .

So