1976 AHSME Problems/Problem 24

Problem

In the adjoining figure, circle $\mathit{K}$ has diameter $\mathit{AB}$ ; circle $\mathit{L}$ is tangent to circle $\mathit{K}$ and to $\mathit{AB}$ at the center of circle $\mathit{K}$ ; and circle $\mathit{M}$ tangent to circle $\mathit{K}$ , to circle $\mathit{L}$ and $\mathit{AB}$ . The ratio of the area of circle $\mathit{K}$ to the area of circle $\mathit{M}$ 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$", M); [/asy]$ $\textbf{(A) }12\qquad \textbf{(B) }14\qquad \textbf{(C) }16\qquad \textbf{(D) }18\qquad \textbf{(E) }\text{not an integer}$

Solution

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
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1976 AHSME Problems/Problem 24

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