Question

if from an external point P of centre O two tangents PQ and PR are drawn such that angle QPR = 120 ,prove that 2 PQ= PO



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Answer 1

Step-by-step explanation:

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.

Answer 2

Step-by-step explanation:

Step-by-step explanation:

<120 is bisected by OP

Hence <OPQ= 60

In triangle OPQ,

Cos 60= 1/2=PQ/OP

2PQ=OP

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