Difference between revisions of "1976 AHSME Problems/Problem 24"
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== Solution == | == Solution == | ||
+ | Let <math>R</math> and <math>r</math> be the radii of circles <math>K</math> and <math>M,</math> respectively. | ||
+ | <asy> | ||
+ | /* Made by Klaus-Anton, Edited by MRENTHUSIASM */ | ||
+ | size(200); | ||
+ | pair K=(0,0),B=(1,0),A=(-1,0),L=(0,0.5),M=(sqrt(2)/2,.25),T=(2*sqrt(2)/3,1/3); | ||
+ | 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, (0,5/4)); | ||
+ | label("$M$", M, (0,5/4)); | ||
+ | dot(K,linewidth(4)); | ||
+ | dot(L,linewidth(4)); | ||
+ | dot(M,linewidth(4)); | ||
+ | dot(T,linewidth(4)); | ||
+ | </asy> | ||
+ | |||
== See Also == | == See Also == | ||
{{AHSME box|year=1976|num-b=23|num-a=25}} | {{AHSME box|year=1976|num-b=23|num-a=25}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 06:26, 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
Solution
Let and
be the radii of circles
and
respectively.
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.