1. 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?
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By: anil on 05 May 2019 02.31 am
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 angle Triangle ABC is similar to triangle AMO. $$frac{(2r+3)}{sqrt{(r+3)^2-r^2}} = frac{9}{r}$$ r = 9/2
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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 angle Triangle ABC is similar to triangle AMO. $$frac{(2r+3)}{sqrt{(r+3)^2-r^2}} = frac{9}{r}$$ r = 9/2