1. ## Geometric word problem

The radio signal from the transmitter site of the radio station WGGW can be received only within a radius of 52 miles in all directions from the transmitter site. A map of the region of coverage of the the radio signal is given in the standard (x,y) coordinate plane, with the transmitter site at the origin and 1 coordinate unit representing 1 miles.

The transmitter site of radio station WGGW and the transmitter site of another radio station, WGWB are on the same highway 100 miles apart. The radio signal from the transmitter site of WGWB can be received only within a radius of 60 miles in all directions from the WGWB transmitter site. Assuming the highway is a straight, for how many miles along the highway can the radio signals of both stations be received?

The solution is 12 but I don't have a clue how they got that as the answer??

2. Hello, donnagir!

What a hideously worded problem!
Why did they explain about circles and the origin and so on?

You drive past station A, which broadcasts for 52 miles.

You drive toward station B (100 miles away) which broadcasts for 60 miles.
Code:
      : - - - 52  - - - :
A*---------*=======*-------------* B
: - - - -  60 - - - - :

: - - - - - - 100 - - - - - - - :

Can you see that the region common to both stations is 12 miles long?

3. Ahhhhh thanks so much for that sketch soroban! Now I see it! Thought it was a bit more involved than that. Since the remaining portion is 40 from radio station B, 40 + x = 52, since the portion that finally remains is 12 to get 52 for radio station A.