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
Ask Download

Transcript

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

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
Jail