MathDB

In the figure,

\overline{AB}

and

\overline{CD}

are diameters of the circle with center

O

\overline{AB} \perp \overline{CD}

, and chord

\overline{DF}

intersects

\overline{AB}

E

. If

DE = 6

and

EF = 2

, then the area of the circle is [asy] size(120); defaultpen(linewidth(0.7)); pair O=origin, A=(-5,0), B=(5,0), C=(0,5), D=(0,-5), F=5*dir(40), E=intersectionpoint(A--B, F--D); draw(Circle(O, 5)); draw(A--B^^C--D--F); dot(O^^A^^B^^C^^D^^E^^F); markscalefactor=0.05; draw(rightanglemark(B, O, D)); label("

A

", A, dir(O--A)); label("

B

", B, dir(O--B)); label("

C

", C, dir(O--C)); label("

D

", D, dir(O--D)); label("

F

", F, dir(O--F)); label("

O

", O, NW); label("

E

", E, SE);[/asy]

<span class='latex-bold'>(A)</span>\ 23\pi \qquad <span class='latex-bold'>(B)</span>\ \dfrac{47}{2}\pi \qquad <span class='latex-bold'>(C)</span>\ 24\pi \qquad <span class='latex-bold'>(D)</span>\ \dfrac{49}{2}\pi \qquad <span class='latex-bold'>(E)</span>\ 25\pi

Problem Statement