# User:Azjps/1951 AHSME Problems/Problem 3

< User:Azjps

Revision as of 11:12, 10 January 2008 by JBL (talk | contribs) (1951 AMC 12 Problems/Problem 3 moved to 1951 AHSME Problems/Problem 3: This problem isn't multiple-choice -- can someone check if it's correct?)

## Problem

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).

## Solution

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.