Construction: Draw a circle (center O) with the given conditions i.e. external point P and two tangents PQ and PR.
To Prove: 2PQ = PO
We know that the radius is perpendicular to the tangent at the point of contact.
⇒ ∠OQP = 90°
We know that the tangents drawn to a circle from an external point are equally inclined to the segment, joining to the centre to that point.
⇒ ∠QPO = 60°
Cos 60° = PQ/PO
⇒ � = PQ/PO
⇒ 2PQ = PO
Ans. Hence, proved that 2PQ = PO.
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