SOLUTION: GPS Satellites orbit 12,500 miles above the surface of the earth. Point A represents the position of a satellite. Line segments AB and AC are externally tangent to the earth touch

Question 161159: GPS Satellites orbit 12,500 miles above the surface of the earth. Point A represents the position of a satellite. Line segments AB and AC are externally tangent to the earth touch the earth at points B and C. Segment AB = 15,977 miles from point A(satellite) to point B(edge of earth). Line segment AE represents a line from the center of the earth to the orbiting satellite. Line segment DE, which is a portion of segment AE, represents the radius of the earth. The question is, What is the radius represented by line segment DE?
If AB = 15,977 then BC also equal 15,977, right... I am not sure how to find the diameter in order to get the radius...
This question if for extra credit and not from a text book...
Thanks for all you help!
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
AB, BE, and AE form a right triangle with the right angle at the point of tangency (B)

BE is the radius (r) of the Earth __ AE is the radius (r) plus the altitude of the satellite

using Pythagoras __ AB^2+BE^2=AE^2 __ 15977^2+r^2=(r+12500)^2 __ 15977^2+r^2=r^2+25000r+12500^2

subtracting r^2+12500^2 __ 15977^2-12500^2=25000r __ dividing by 25000 __ 3961=r (approx)
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