1995 AIME Problems/Problem 9
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
Let , $\angleCDM=3x$ (Error compiling LaTeX. ! Undefined control sequence.). 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 .