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TWO TANGENT SEGMENTS BC,BD ARE DRAWN TO A CIRCLE WITH A CENTRE O SUCH THAT

 BC and BD are tangents with ?DBC = 120

  ( tangent from an external point are equally inclined to the segment joining the centre to that point).

Now in ?BCO

Cos 60 = BC/OB.

1/2 = BC/OB.

OB = 2BC = BC + BC

OB = BC + BD

(BC = BD as tangents drawn from an external point to a circle are equal).