1975 AHSME Problems/Problem 28
Revision as of 22:58, 12 February 2021 by Justinlee2017 (talk | contribs) (Created page with "==Solution== Here, we use Mass Points. Let <math>AF = x</math>. We then have <math>AE = 2x</math>, <math>EC = 16-2x</math>, and <math>FB = 12 - x</math> Let <math>B</math> hav...")
Solution
Here, we use Mass Points.
Let . We then have
,
, and
Let
have a mass of
. Since
is the midpoint,
also has a mass of
.
Looking at segment
, we have
So
Looking at segment
,we have
So
From this, we get
and
We want the value of
. This can be written as
Thus
~JustinLee2017