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Ex 10.2, 2 - In fig, if TP and TQ are two tangents to a - Theorem 10.1: Tangent perpendicular to radius (numerical type)

  1. Chapter 10 Class 10 Circles
  2. Serial order wise
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Ex 10.2,2 Choose the correct option and give justification. In figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠ PTQ is equal to 60° (B) 70° (C) 80° (D) 90° Given ∠ POQ = 110° Here TP is a tangent. So, OP ⊥ TP Hence, ∠ OPT = 90° Similarly , TQ is a tangent. So, OQ ⊥ TQ Hence, ∠ OQT = 90° Now, In quadrilateral TPOQ ∠PTO + ∠ OQT + ∠ PTQ + ∠ POQ = 360° Putting values 90° + 90° + ∠PTQ + 110° = 360° 90° + 90° + 110° + ∠PTQ = 360° 290° + ∠PTQ = 360° ∠PTQ = 360° – 290° ∠ PTQ = 70° Hence, ∠ PTQ = 70° Thus, Option (B) is correct

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