Three towns in Ireland -- Poole, Bray, and Alton -- are located 8, 3, and 5 miles, respectively, from a store. How far apart are the towns from one another if they are located at the vertices of an equilateral triangle?
You may want to make a GSP file to model the situation.
Is the store inside, on, or outside the triangle?
Compare with the Barn problem (Distance from the Nearest Road).
Consider the problem if the three distances are 5, 7, and 8 units.
Consider the problem if the three distances are 1, 2, and 3 units (Sastry, 1997).
Hunter, J. A. H. 100 Mathematics Problems; Problem #99.
Sastry, K. R. S. (1997) Problem proposal 340. Mathematics and Computer Education, 31, p. 195.