Q. 84.4( 19 Votes )

If from an extern

Answer :


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°

Consider ΔQPO,

Cos 60° = PQ/PO

� = PQ/PO

2PQ = PO

Ans. Hence, proved that 2PQ = PO.

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