Last updated at Feb. 25, 2017 by Teachoo

Transcript

Example 17 A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected? Let P be the pole Gates A & B are diametrically opposite So, AB = Diameter of circle = 13 m Also given that, Difference of the distance of the pole from the two gates is 7 metres BP – AP or AP – BP is 7 m Let us take AP – BP = 7 i.e. AP = BP + 7 Let BP = x So, AP = BP + 7 = x + 7 Now, Since AB is a diameter ∠ APB = 90° Now, Δ APB is a right angle triangle Using Pythagoras theorem Hypotenuse2 = Height2 + Base2 BP2 + AP2 = AB2 x2 + (x + 7)2 = 132 x2 + x2 + 49 + 2×𝑥×7=169 x2 + x2 + 49 + 14x = 169 2x2 + 14x + 49 – 169 = 0 2x2 + 14x – 120 = 0 Divide the equation by 2 2𝑥2/2+14𝑥/2−120/2 = 0 x2 + 7x – 60 = 0 Comparing equation with ax2 + bx + c = 0 Here, a = 1, b = 7, c = – 60 We know that D = b2 – 4ac D = (7)2 – 4×(1)×(−60) = 49 – 4×(−60) = 49 + 240 = 289 Hence , roots to equation are x = (−𝑏 ± √𝐷)/2𝑎 Putting values x = (− 7 ± √289)/(2 × 1) x = (− 7 ± 17 )/2 Solving So, x = 5, & x = –12 Since x is distance, it must be positive Hence, x = 5. Hence, BP = x = 5 m & AP = x + 7 = 5 + 7 = 12 m

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 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/.