CBSE Class 10 Answered
question
Asked by arindeep.singh | 02 Oct, 2020, 01:19: PM
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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