Difference between revisions of "2013 AIME II Problems/Problem 4"
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Revision as of 15:44, 4 April 2013
The distance from point to point is . The vector that starts at point A and ends at point B is given by . Since the center of an equilateral triangle, , is also the intersection of the perpendicular bisectors of the sides of the triangle, we need first find the equation for the perpendicular bisector to . The line perpendicular to through the midpoint, , can be parameterized by . At this point, it is useful to note that is a 30-60-90 triangle with measuring . This yields the lenght of to be . Therefore, . Therefore yielding an answer of .