MathDB

[asy] size(2.5inch); pair A = (-2,0), B = 2dir(150), D = (2,0), C; draw(A..(0,2)..D--cycle); C = intersectionpoint(A..(0,2)..D,Circle(B,arclength(A--B))); draw(A--B--C--D--cycle); label("

A

",A,W); label("

B

",B,NW); label("

C

",C,N); label("

D

",D,E); label("

4

",A--D,S); label("

1

",A--B,E); label("

1

",B--C,SE); //Credit to chezbgone2 for the diagram[/asy]
Quadrilateral

ABCD

is inscribed in a circle with side

AD

, a diameter of length

4

. If sides

AB

and

BC

each have length

1

, then side

CD

has length

<span class='latex-bold'>(A) </span>\frac{7}{2}\qquad<span class='latex-bold'>(B) </span>\frac{5\sqrt{2}}{2}\qquad<span class='latex-bold'>(C) </span>\sqrt{11}\qquad<span class='latex-bold'>(D) </span>\sqrt{13}\qquad <span class='latex-bold'>(E) </span>2\sqrt{3}

Problem Statement