A village has a circular wall around it, and the wall has four gates pointing north, south east and west. A tree stands outside the village, 16 m north of the north gate, and it can be just seen appearing on the horizon from a point 48 m ea

Question

A village has a circular wall around it, and the wall has four gates pointing north, south east and west. A tree stands outside the village, 16 m north of the north gate, and it can be just seen appearing on the horizon from a point 48 m east of the south gate. What is the diameter in meters, of the wall that surrounds the village?

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Correct answer: 48

Let radius equals to r aligned & A B= A O^2-O B^2 = (16+r)^2-r^2 = 256+32 r & A D^2+C D^2=A C^2 aligned aligned & (48)^2+(2 r+16)^2=(48+ 256+32 r )^2 & r^2+8 r=24 256+32 r & r(r+8)_ - =24 4 2 r+8 & r r+8 =24 32 & r=24 aligned Diameter equal to 48

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