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Circle problem

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Circle problem

by Uri » Mon Mar 09, 2009 1:44 am
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

Image

OA: [spoiler](B)[/spoiler]
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by bluementor » Mon Mar 09, 2009 2:25 am
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-
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