Question 116906: 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, three miles north of the north gate, and it can just be seen from a point nine miles east of the south gate. The problem is to find the diameter of the wall that surrounds the city.
Answer by kev82(151)   (Show Source):
You can put this solution on YOUR website! OK, I'll start you off on this, have a go after what I've said and then mail back and let us know where you've got to.
1) The city wall is a circle (says so in problem)
2) If we can find radius of the circle, we can solve the problem
3) We can assume the center of the city(circle) is at coordinates (0,0)
4) The coordinates of the house are (0, r+3)
5) The coordinates of the point we can 'just' see the house from are (-9,-r)
Make sure you agree with points 1 through 5. Now, ask yourself what does it mean in the question when it says 'and it can just be seen'. What does this tell you about line between the house and where we can see it from and the circle? Can you write this something down as an equuation and solve for r?
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