MathDB
Math Prize 2011 Problem 20

Source:

September 19, 2011
probabilitytrigonometryconicsellipserotationgeometrygeometric transformation

Problem Statement

Let ABCABC be an equilateral triangle with each side of length 1. Let XX be a point chosen uniformly at random on side AB‾\overline{AB}. Let YY be a point chosen uniformly at random on side AC‾\overline{AC}. (Points XX and YY are chosen independently.) Let pp be the probability that the distance XYXY is at most 134 \dfrac{1}{\sqrt[4]{3}}\,. What is the value of 900p900p, rounded to the nearest integer?
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