MathDB

A rectangle intersects a circle as shown:

AB=4

BC=5

, and

DE=3

. Then

EF

equals:
[asy]size(200); defaultpen(linewidth(0.7)+fontsize(10)); pair D=origin, E=(3,0), F=(10,0), G=(12,0), H=(12,1), A=(0,1), B=(4,1), C=(9,1), O=circumcenter(B,C,F); draw(D--G--H--A--cycle); draw(Circle(O, abs(O-C))); label("

A

", A, NW); label("

B

", B, NW); label("

C

", C, NE); label("

D

", D, SW); label("

E

", E, SE); label("

F

", F, SW);
label("4", (2,0.85), N); label("3", D--E, S); label("5", (6.5,0.85), N); [/asy]

\mathbf{(A)}\; 6\qquad \mathbf{(B)}\; 7\qquad \mathbf{(C)}\; \frac{20}3\qquad \mathbf{(D)}\; 8\qquad \mathbf{(E)}\; 9

Problem Statement