Difference between revisions of "User:Azjps/1951 AHSME Problems/Problem 3"
(by correct, do you mean the answer or the question? The answer's right, duno about the question) |
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==Problem== | ==Problem== | ||
− | + | [[Point]]s <math>A</math> and <math>B</math> are selected on the graph of <math>y=-1/2x^2</math> so that triangle <math>ABO</math> is [[equilateral triangle|equilateral]]. Find the length of one side of triangle <math>ABO</math> (point <math>O</math> is at the origin). | |
== Solution == | == Solution == | ||
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==See Also== | ==See Also== | ||
− | + | {{AHSME box|year=1951|num-b=2|num-a=4}} | |
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[[Category:Introductory Geometry Problems]] | [[Category:Introductory Geometry Problems]] |
Revision as of 19:38, 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.
See Also
1951 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |