UFO Question

Question

A giant spherical UFO comes to earth and lands in soft dirt, thus pressing the dirt down in the shape of the UFO. When the UFO takes off, you measure the indentation left behind which is of course in the shape of a huge circle. The circle is 100 feet in diameter and the indentation is 10 feet deep at the deepest point. What is the radius of the UFO?

 

After you have solved problem #1, you are called in to locate the transmitter that the aliens on earth used to contact the UFO. So, you get a map of the bay area and draw a coordinate axis on it. Then you get a couple radio receivers and set them to pick up the alien radio signal and measure the signal's strength. You assume that if the signal bass the same strength at two different points, then they must be the same distance from the transmitter. Then you drive around the bay area and measure the signal strength at different places. (This is called triangulating.)

 

You find out that the signal at (7,-3) and (1,3) is the same. Also, the signal is the same at (6,3) and (3,-6). Where is the transmitter located?