1995 AIME Problems/Problem 9
Problem
Triangle is isosceles, with
and altitude
Suppose that there is a point
on
with
and
Then the perimeter of
may be written in the form
where
and
are integers. Find
Solution
Let , $\angleCDM=3x$ (Error compiling LaTeX. Unknown error_msg). Then,
. Expanding tan 3x using the angle sum formula gives
. Thus,
. Solving, we get
. Hence,
and AC=
by Pythag. The total perimeter is double the sum of these, which is
. The answer is then
.