Difference between revisions of "User:Azjps/1951 AHSME Problems/Problem 3"
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==See Also== | ==See Also== | ||
* [[1951 AHSME]] | * [[1951 AHSME]] | ||
− | * [[ | + | * [[1951 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.