If from an external point P of a circle with centre O, two tangents PQ and PR are drawn such that ∠QPR = 120°, prove that 2PQ = PO.
Let us draw the circle with external point P and two tangents PQ and PR.
We know that the radius is perpendicular to the tangent at the point of contact.
We also know that the tangents drawn to a circle from an external point are equally inclined to the segment, joining the centre to that point.
Now in ∆QPO: