MathDB

In this diagram the center of the circle is

O

, the radius is

a

inches, chord

EF

is parallel to chord

CD, O, G, H, J

are collinear, and

G

is the midpoint of

CD

. Let

K

(sq. in.) represent the area of trapezoid

CDFE

and let

R

(sq. in.) represent the area of rectangle

ELMF

. Then, as

CD

and

EF

are translated upward so that

OG

increases toward the value

a

, while

JH

always equals

HG

, the ratio

K:R

become arbitrarily close to: [asy] size((270)); draw((0,0)--(10,0)..(5,5)..(0,0)); draw((5,0)--(5,5)); draw((9,3)--(1,3)--(1,1)--(9,1)--cycle); draw((9.9,1)--(.1,1)); label("O", (5,0), S); label("a", (7.5,0), S); label("G", (5,1), SE); label("J", (5,5), N); label("H", (5,3), NE); label("E", (1,3), NW); label("L", (1,1), S); label("C", (.1,1), W); label("F", (9,3), NE); label("M", (9,1), S); label("D", (9.9,1), E); [/asy]

<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ \sqrt{2} \qquad<span class='latex-bold'>(D)</span>\ \frac{1}{\sqrt{2}}+\frac{1}{2} \qquad<span class='latex-bold'>(E)</span>\ \frac{1}{\sqrt{2}}+1

Problem Statement