Question 11
A certain city has a circular wall around it, and this wall has four gates pointing north, south, east and west. A house stands outside the city, 3 km north of the north gate, and it can just be seen from a point 9 km east of the south gate. What is the diameter of the wall that surrounds the city?
Solution
B is the south gate. A is the house and BC = 9 km.
In triangle ABC and triangle AMO
ABC = OMA = 90 degree
BAC = OAM = Common angleÂ
Triangle ABC is  similar to triangle AMO.
$$\frac{(2r+3)}{\sqrt{(r+3)^2-r^2}} = \frac{9}{r}$$
r = 9/2
Create a FREE account and get:
- All Quant CAT complete Formulas and shortcuts PDF
- 35+ CAT previous papers with video solutions PDF
- 5000+ Topic-wise Previous year CAT Solved Questions for Free
CAT Quant Questions | CAT Quantitative Ability
CAT Linear Equations QuestionsCAT Quadratic Equations QuestionsCAT Logarithms QuestionsCAT Number Systems QuestionsCAT Arithmetic Questions
CAT DILR Questions | LRDI Questions For CAT
CAT Coins and Weights QuestionsCAT Truth Lie Concept QuestionsCAT Games and Tournamnents QuestionsCAT 2D & 3D LR QuestionsCAT Puzzles Questions
