Question

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Answer 1

Hope this helps you.......

Answer 2

Heya !!

Refer to the attachment for the diagram.

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Given :- A circle with centre O, an external point T and two tangents TP and TQ to the circle, where P, Q are the points of contact.

To prove :- angle PTQ = 2 angle OPQ

Proof :- Let angle PTQ = A

Lengths of tangents from an external point are equal. So, TP = TQ.
Therefore, TPQ is an isosceles ∆.

Now, angle TPQ = angle TQP = 1/2(180° –A)
=> 90° – (1/2)

Tangent at any point of a circle is perpendicular to the radius through the point of contact. So, angle OPT = 90°

Now, angle OPQ = angle OPT – angle TPQ
=> 90° – [ 90° – (1/2)A ]
=> 1/2 × A
=> 1/2 × angle PTQ

Therefore, angle PTQ = 2 angle OPQ

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