Difference between revisions of "1976 AHSME Problems/Problem 24"
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== Problem == | == Problem == | ||
| − | In the adjoining figure, circle <math> | + | In the adjoining figure, circle <math>K</math> has diameter <math>AB</math>; circle <math>L</math> is tangent to circle <math>K</math> and to <math>AB</math> at the center of circle <math>K</math>; and circle <math>M</math> tangent to circle <math>K</math>, to circle <math>L</math> and <math>AB</math>. The ratio of the area of circle <math>K</math> to the area of circle <math>M</math> is |
| − | and to <math> | ||
| − | to circle <math> | ||
<asy> | <asy> | ||
/* Made by Klaus-Anton, Edited by MRENTHUSIASM */ | /* Made by Klaus-Anton, Edited by MRENTHUSIASM */ | ||
| Line 19: | Line 17: | ||
\textbf{(C) }16\qquad | \textbf{(C) }16\qquad | ||
\textbf{(D) }18\qquad | \textbf{(D) }18\qquad | ||
| − | \textbf{(E) }\text{not an integer} | + | \textbf{(E) }\text{not an integer}</math> |
== Solution == | == Solution == | ||
Revision as of 05:49, 6 September 2021
Problem
In the adjoining figure, circle 
has diameter 
; circle 
is tangent to circle and to at the center of circle ; and circle 
tangent to circle , to circle and . The ratio of the area of circle to the area of circle is
![[asy] /* Made by Klaus-Anton, Edited by MRENTHUSIASM */ size(150); pair K=(0,0),B=(1,0),A=(-1,0),L=(0,0.5),M=(sqrt(2)/2,.25); draw(circle(K,1)^^A--B); draw(circle(L,0.5)^^circle(M,.25)); label("$A$", A, W); label("$K$", K, S); label("$B$", B, E); label("$L$", L); label("$M$", M); [/asy]](http://latex.artofproblemsolving.com/7/b/0/7b0c55f990d80458f68a73509b9da6016ca29e1b.png)
Solution
See Also
| 1976 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
