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CBSE Class 10 Answered

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Asked by arindeep.singh | 02 Oct, 2020, 01:19: PM
answered-by-expert Expert Answer

Question: Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.

Solution: 

We know that tangent to a circle is perpendicular to its radius at the point of contact.

So, ∠OPT = ∠OQT = 90o

In quadrilateral POQT, we have

∠OPT + ∠PTQ + ∠OQT + ∠POQ = 360o

 ∠PTQ = 180o - ∠POQ

= ∠1 + ∠2 (Using angle sum property in △POQ)

= 2∠1 (∠1 = ∠2 as OP = OQ)

= 2∠OPQ

Answered by Renu Varma | 03 Oct, 2020, 03:57: PM

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