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Two tangents TP and TQ are drawn to a circle with centre O from an internal point T. if angle PTQ=x and angle OPQ=y, thenPlease step by step kar dijiye koi |
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Answer» We know that, the lengths of tangents drawn from an external point to a circle are equal. ∴ TP = TQ In ΔTPQ, TP = TQ ⇒ ∠TQP = ∠TPQ ...(1) (In a triangle, equal sides have equal angles opposite to them) ∠TQP + ∠TPQ + ∠PTQ = 180º (Angle sum PROPERTY) ∴ 2 ∠TPQ + ∠PTQ = 180º (Using(1)) ⇒ ∠PTQ = 180º – 2 ∠TPQ ...(1) We know that, a tangent to a circle is perpendicular to the radius through the point of contact. OP ⊥ PT, ∴ ∠OPT = 90º ⇒ ∠OPQ + ∠TPQ = 90º ⇒ ∠OPQ = 90º – ∠TPQ ⇒ 2∠OPQ = 2(90º – ∠TPQ) = 180º – 2 ∠TPQ ...(2) From (1) and (2), we get ∠PTQ = 2∠OPQ Hope it HELPS!! Thank u |
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