MathDB

In circle

O

chord

AB

is produced so that

BC

equals a radius of the circle.

CO

is drawn and extended to

D

AO

is drawn. Which of the following expresses the relationship between

x

and

y

?
[asy]size(200);defaultpen(linewidth(0.7)+fontsize(10)); pair O=origin, D=dir(195), A=dir(150), B=dir(30), C=B+1*dir(0); draw(O--A--C--D); dot(A^^B^^C^^D^^O); pair point=O; label("

A

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

B

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

C

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

D

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

O

", O, dir(285)); label("

x

", O+0.1*dir(172.5), dir(172.5)); label("

y

", C+0.4*dir(187.5), dir(187.5)); draw(Circle(O,1)); [/asy]
(A)\ x\equal{}3y \\ (B)\ x\equal{}2y \\ (C)\ x\equal{}60^\circ \\ (D)\ \text{there is no special relationship between }x\text{ and }y \\ (E)\ x\equal{}2y \text{ or }x\equal{}3y\text{, depending upon the length of }AB

Problem Statement