In Figure, two tangents `A Ba n dA C` are drawn to a circle with centre `O` such that `/_B A C=120^0dot` Prove that `O A=2A B`

Explanation

`/_BAC=120^0` (given)

`AB=AC` ( tangents on the circle from external point A)

`OB=OC `(Radius to the circle)

`:. /_BAO =/_CAO=60^0 `(angle bisector)

In `/_\ABO`

`cosA = (AB)/(OA`)

`:.cos60^0=(AB)/(OA`)

`:.1/2=(AB)/(OA)`

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