Last updated at May 29, 2018 by Teachoo

Transcript

Ex 10.2,9 In figure, XY and X′Y′ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X′Y′at B. Prove that ∠AOB = 90°. Given : XY is a tangent at point P and X’Y’ is a tangent at point Q And XY ∥ X’Y’ AB is a tangent at point C To prove: ∠ AOB = 90° Proof: Join OC For tangent AB & Radius OC OC ⊥ AB So, ∠ ACO = ∠ BCO = 90° In Δ AOP & Δ AOC OP = OC AP = AC OA = OA ∴ Δ AOC ≅ Δ AOP So, ∠ AOP= ∠ AOC Now In Δ BOC & Δ BOQ OC = OQ BC = BQ OB = OB ∴ Δ BOC ≅ Δ BOQ So, ∠ BOC = ∠ BOQ For line PQ ∠ AOP + ∠ AOC + ∠ BOC + ∠ BOQ = 180° ∠ AOC + ∠ AOC + ∠ BOC + ∠ BOC = 180° 2∠ AOC + 2∠ BOC = 180° 2(∠ AOC + ∠ BOC) = 180° ∠ AOC + ∠ BOC = (180°)/2 ∠ AOC + ∠ BOC = 90° ∠ AOB = 90° Hence proved

Class 10

Important Questions for Exam - Class 10

- Chapter 1 Class 10 Real Numbers
- Chapter 2 Class 10 Polynomials
- Chapter 3 Class 10 Pair of Linear Equations in Two Variables
- Chapter 4 Class 10 Quadratic Equations
- Chapter 5 Class 10 Arithmetic Progressions
- Chapter 6 Class 10 Triangles
- Chapter 7 Class 10 Coordinate Geometry
- Chapter 8 Class 10 Introduction to Trignometry
- Chapter 9 Class 10 Some Applications of Trignometry
- Chapter 10 Class 10 Circles
- Chapter 11 Class 10 Constructions
- Chapter 12 Class 10 Areas related to Circles
- Chapter 13 Class 10 Surface Areas and Volumes
- Chapter 14 Class 10 Statistics
- Chapter 15 Class 10 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.