If A is the center of the circle shown below and AB=BC=CD, what is the value of x?
(A) 15
(B) 30
(C) 45
(D) 60
(E) 75
OA: [spoiler](B)[/spoiler]
(A) 15
(B) 30
(C) 45
(D) 60
(E) 75
OA: [spoiler](B)[/spoiler]
AB = BC, and since AB=AC (i.e. radius of the circle), triangle ABC must be equilateral. Angle ABC = 60.
Since, AB=BC=CD=AD, then ABCD is a rhombus, and line BD actually cuts the angle ABC by half. So half of angle ABC = 60*0.5 = 30. Choose B.
-BM-
