Difference between revisions of "1991 AHSME Problems/Problem 22"
(Created page with "== Problem == <asy> draw(circle((0,0),10),black+linewidth(.75)); MP(")",(0,0),S); </asy> Two circles are externally tangent. Lines <math>\overline{PAB}</math> and <math>\overli...") |
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== Problem == | == Problem == | ||
<asy> | <asy> | ||
− | draw(circle((0,0), | + | draw(circle((0,6sqrt(2)),2sqrt(2)),black+linewidth(.75)); |
− | MP(")",(0,0),S); | + | draw(circle((0,3sqrt(2)),sqrt(2)),black+linewidth(.75)); |
+ | draw((-8/3,16sqrt(2)/3)--(-4/3,8sqrt(2)/3)--(0,0)--(4/3,8sqrt(2)/3)--(8/3,16sqrt(2)/3),dot); | ||
+ | MP("B",(-8/3,16*sqrt(2)/3),W);MP("B'",(8/3,16*sqrt(2)/3),E); | ||
+ | MP("A",(-4/3,8*sqrt(2)/3),W);MP("A'",(4/3,8*sqrt(2)/3),E); | ||
+ | MP("P",(0,0),S); | ||
</asy> | </asy> | ||
− | Two circles are externally tangent. Lines <math>\overline{PAB}</math> and <math>\overline{PA'B'}</math> are common tangents with <math>A</math> and <math>A'</math> on the smaller circle <math>B</math> and <math>B'</math> on the larger circle. If <math>PA=AB=4</math>, then the | + | Two circles are externally tangent. Lines <math>\overline{PAB}</math> and <math>\overline{PA'B'}</math> are common tangents with <math>A</math> and <math>A'</math> on the smaller circle <math>B</math> and <math>B'</math> on the larger circle. If <math>PA=AB=4</math>, then the area of the smaller circle is |
<math>\text{(A) } 1.44\pi\quad | <math>\text{(A) } 1.44\pi\quad |
Revision as of 14:48, 28 September 2014
Problem
Two circles are externally tangent. Lines and are common tangents with and on the smaller circle and on the larger circle. If , then the area of the smaller circle is
Solution
See also
1991 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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.