2 tangents QA and QB are drawn to the circle wit centre O such that <AQB = 60 with AQ = 3 cm, find OQ pls help Share with your friends Share 1 Manbar Singh answered this We know that, tangents drawn from an external point to a circle are equal in lengths.So, QA = QB ......1We know that, tangent to the circle is always ⊥ to the radius at the point of contact.So, ∠OAQ = ∠OBQ = 90° .......2In ∆OAQ and ∆OBQ,∠OAQ = ∠OBQ Using 2 OQ = OQ common QA = QB Using 1⇒∆OAQ ≅ ∆OBQ RHS⇒∠OQA = ∠OQB CPCT⇒∠OQA = ∠OQB = 12∠AQB = 12×60° = 30°In ∆OAQ,cos 30° = basehypotenuse = AQOQ⇒32 = 3OQ⇒OQ = 23 cm 2 View Full Answer
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