Problem

1991 AHSME Problem 22

[asy] draw(circle((0,6sqrt(2)),2sqrt(2)),black+linewidth(.75)); 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]

Two circles are externally tangent. Lines \overline{PAB} and \overline{PA'B'} are common tangents with A and A' on the smaller circle B and B' on the larger circle. If PA=AB=4, then the area of the smaller circle is

\textbf{(A) } 1.44\pi\qquad \textbf{(B) } 2\pi\qquad \textbf{(C) } 2.56\pi\qquad \textbf{(D) } \sqrt{8}\pi\qquad \textbf{(E) } 4\pi

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.


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Category: AHSME
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