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Last updated at March 2, 2017 by Teachoo

Transcript

Ex 10.4, 4 If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see figure). Given: Two concentric circles with centre O. & a line intersects the circles at A,B,C & D To prove: AB = CD Proof: Let two circles be C1 & C2 and line be l We draw OP perpendicular to line l In circle C1, OP ⊥ BC So, OP bisects BC, i.e. BP = CP (As OP is perpendicular to line l ) (Perpendicular drawn from centre of a circle to a chord bisects the chord) In circle C2, OP ⊥ AD So, OP bisects AD, i.e. AP = DP (As OP is perpendicular to line l ) (Perpendicular drawn from centre of a circle to a chord bisects the chord) Subtracting (2) & (1), (2) – (1) AP – BP = DP – CP ⇒ AB = CD Hence proved

Class 9

Important Questions for Exam - Class 9

- Chapter 1 Class 9 Number Systems
- Chapter 2 Class 9 Polynomials
- Chapter 3 Class 9 Coordinate Geometry
- Chapter 4 Class 9 Linear Equations in Two Variables
- Chapter 5 Class 9 Introduction to Euclid's Geometry
- Chapter 6 Class 9 Lines and Angles
- Chapter 7 Class 9 Triangles
- Chapter 8 Class 9 Quadrilaterals
- Chapter 9 Class 9 Areas of parallelograms and Triangles
- Chapter 10 Class 9 Circles
- Chapter 11 Class 9 Constructions
- Chapter 12 Class 9 Herons Formula
- Chapter 13 Class 9 Surface Areas and Volumes
- Chapter 14 Class 9 Statistics
- Chapter 15 Class 9 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.