2014 AIME II Problems/Problem 11
Problem 11
In ,
and
. $\abs{RD}=1$ (Error compiling LaTeX. Unknown error_msg). Let
be the midpoint of segment
. Point
lies on side
such that
. Extend segment
through
to point
such that
. Then
, where
and
are relatively prime positive integers, and
is a positive integer. Find
.
Solution
Let be the foot of the perpendicular from
to
, so
. Since triangle
is isosceles,
is the midpoint of
, and
. Thus,
is a parallelogram and
.
We can then use coordinates to find that , so the answer is
.