User:Azjps/1951 AHSME Problems/Problem 3
Points and are selected on the graph of so that triangle is equilateral. Find the length of one side of triangle (point is at the origin).
The parabola opens downward, and by symmetry we realize that the y-coordinates of are the same. Thus the segments will have slope . Without loss of generality consider the equation of (we let be in the third quadrant), which has equation . This intersects the graph of at ; we drop zero so . The length of a side of the triangle is . We can now easily verify that this triangle indeed is equilateral.