# Difference between revisions of "User:Azjps/1951 AHSME Problems/Problem 3"

m (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?) |
(ugh, this needs a lot of work...) |
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==See Also== | ==See Also== | ||

− | * [[1951 | + | * [[1951 AHSME]] |

− | * [[1952 | + | * [[1952 AHSME Problems/Problem 4 | Next problem]] |

[[Category:Introductory Geometry Problems]] | [[Category:Introductory Geometry Problems]] |

## Revision as of 11:21, 10 January 2008

## 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.