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Please, help to solve the question!!!

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Senior Manager
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Please, help to solve the question!!! [#permalink] New post 23 Mar 2007, 06:13
Can anybody help to solve the problem solving question???
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Director
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 [#permalink] New post 23 Mar 2007, 06:25
I think it is (B).

ABC is equilateral => angle A = angle B = angle C = 60
ACD is also equilateral => angle A = angle B = angle C = 60
=> angle A in ABD = 120
AB = AD => ABD is isosceles => angle B = angle D = 180 - 120 / 2 = 30 :-D
Manager
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 [#permalink] New post 23 Mar 2007, 11:44
Yes you are right its 30. I HATED this question I had no idea how to do it. I am not sure how to prove that the arc of BC is equal to the radius, but it is, and thus BAC is 60 and the answer is B 30.
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 [#permalink] New post 24 Mar 2007, 08:39
IMO, the answer is 30 degree.

AB = BC = AC => ABC is an equilateral triangle=> angle BAC is 60 degree
that means angle DAC = 60 degree
As per the rule - angle made by the arc on center is twice the angle made by the same arc on the circumference. Here the angle DAC made by the arc DC on the center is 60 degree. So the DBC = 30.
As angle ABC = 60 degree, the angle ABD = x = 30 degree
Manager
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 [#permalink] New post 24 Mar 2007, 14:00
from given info and figure it is clear that AB=BC=AC=AD=DC. Here basically BD connects two opposite vertices of 2 equi. triangles with common base AC. Hence, it should be dividing the the angles B and D into half. i.e. 60/2 = 30
Senior Manager
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 [#permalink] New post 25 Mar 2007, 21:29
Thanks a lot :shock: !!!!
  [#permalink] 25 Mar 2007, 21:29
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