Mock AIME I 2012 Problems/Problem 3
Problem
Triangle has
,
,
. The trisection points of
are
and
, with
. Segments
and
are extended to points
and
such that
and
. The area of pentagon
is
, where
and
are relatively prime positive integers. Find
.
Solution
Use Heron's formula to find . Also note from the trisection that
. Now
. Similarly,
. From this we deduce that
(i)
(ii) Similarly to (i),
(iii) with ratio
, so
The area of our pentagon is . The answer is
.