Problem

1982 AHSME Problem 14

In the adjoining figure, points B and C lie on line segment AD, and AB, BC, and CD are diameters of circle O, N, and P, respectively. Circles O, N, and P all have radius 15 and the line AG is tangent to circle P at G. If AG intersects circle N at points E and F, then chord EF has length

[asy] size(250); defaultpen(fontsize(10)); pair A=origin, O=(1,0), B=(2,0), N=(3,0), C=(4,0), P=(5,0), D=(6,0), G=tangent(A,P,1,2), E=intersectionpoints(A--G, Circle(N,1))[0], F=intersectionpoints(A--G, Circle(N,1))[1]; draw(Circle(O,1)^^Circle(N,1)^^Circle(P,1)^^G--A--D, linewidth(0.7)); dot(A^^B^^C^^D^^E^^F^^G^^O^^N^^P); label("$A$", A, W); label("$B$", B, SE); label("$C$", C, NE); label("$D$", D, dir(0)); label("$P$", P, S); label("$N$", N, S); label("$O$", O, S); label("$E$", E, dir(120)); label("$F$", F, NE); label("$G$", G, dir(100));[/asy]

\text {(A)} 20 \qquad \text {(B)} 15\sqrt{2} \qquad \text {(C)} 24 \qquad \text{(D)} 25 \qquad \text {(E)} \text{none of these}

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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