Calling the three villages by their initial letters, it is clear that
the three roads form a triangle, A, B, C, with a perpendicular,
measuring twelve miles, dropped from C to the base A, B.
This divides our triangle into two right-angled triangles with a
twelve-mile side in common.
It is then found that the distance from A to C is 15 miles, from C to B
20 miles, and from A to B 25 (that is 9 and 16) miles.
These figures are easily proved, for the square of 12 added to the
square of 9 equals the square of 15, and the square of 12 added to the
square of 16 equals the square of 20.