Difference between revisions of "1992 AHSME Problems/Problem 11"
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− | == Solution == | + | == Solution (Similarity) == |
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+ | We are given that <math>BC</math> is tangent to the smaller circle. Using that, we know where the circle intersects <math>BC</math>, it creates a right triangle. We can also point out that since <math>AC</math> is the diameter of the bigger circle and triangle <math>ABC</math> is inscribed the semi-circle, that angle <math>B</math> is a right angle. Therefore, we have <math>2</math> similar triangles. | ||
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<math>\fbox{B}</math> | <math>\fbox{B}</math> | ||
Revision as of 11:52, 24 November 2016
Problem
The ratio of the radii of two concentric circles is . If
is a diameter of the larger circle,
is a chord of the larger circle that is tangent to the smaller circle, and
, then the radius of the larger circle is
Solution (Similarity)
We are given that is tangent to the smaller circle. Using that, we know where the circle intersects
, it creates a right triangle. We can also point out that since
is the diameter of the bigger circle and triangle
is inscribed the semi-circle, that angle
is a right angle. Therefore, we have
similar triangles.
See also
1992 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.