If from a external point P of a circle with centre O, two tangents PQ and PRare drawn such that angle of QPR=120. prove tht 2PQ=PO.

Here is the answer to your query.

**Given : **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 ΔBCO

⇒ OB = 2BC = BC + BC

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