Question

If from external point P of a circle with centre O , two tangents PQ and PR are drawn such that angle QPR is 120° , prove that 2PQ = PO

Answer 1

Answer:

Step-by-step explanation:

<120 is bisected by OP

Hence <OPQ= 60

In triangle OPQ,

Cos 60= 1/2=PQ/OP

2PQ=OP

H. P.

Answer 2

Hence proved that 2PQ = PO

Step-by-step explanation:

As we know that r(radius) is drawn ⊥ to the tangent at the site of the contact,

So, ∠OQP = 90°

We know also that the tangents which are constructed from the external point of a circle are proportionately bent to the segment in order to link the point to the center;

so, ∠QPO = 60°

In ΔQPO,

Cos60° = PQ/PO

1/2 = PQ/PO

∵ 2PQ = PO

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