Difference between revisions of "1964 AHSME Problems/Problem 36"
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In this figure the radius of the circle is equal to the altitude of the equilateral triangle <math>ABC</math>. The circle is made to roll along the side <math>AB</math>, remaining tangent to it at a variable point <math>T</math> and intersecting lines <math>AC</math> and <math>BC</math> in variable points <math>M</math> and <math>N</math>, respectively. Let <math>n</math> be the number of degrees in arc <math>MTN</math>. Then <math>n</math>, for all permissible positions of the circle: | In this figure the radius of the circle is equal to the altitude of the equilateral triangle <math>ABC</math>. The circle is made to roll along the side <math>AB</math>, remaining tangent to it at a variable point <math>T</math> and intersecting lines <math>AC</math> and <math>BC</math> in variable points <math>M</math> and <math>N</math>, respectively. Let <math>n</math> be the number of degrees in arc <math>MTN</math>. Then <math>n</math>, for all permissible positions of the circle: | ||
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+ | ==See Also== | ||
+ | {{AHSME 40p box|year=1964|num-b=35|num-a=37}} | ||
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+ | [[Category:Introductory Algebra Problems]] | ||
+ | |||
+ | {{MAA Notice}} |
Revision as of 23:18, 24 July 2019
Problem
In this figure the radius of the circle is equal to the altitude of the equilateral triangle . The circle is made to roll along the side , remaining tangent to it at a variable point and intersecting lines and in variable points and , respectively. Let be the number of degrees in arc . Then , for all permissible positions of the circle:
See Also
1964 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 35 |
Followed by Problem 37 | |
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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.