Between Massena and Anaheim there are two railroad tracks. One of them is straight and is 4 miles long. The other one is the arc of a circle and is 5 miles long.

What is the radius of curvature of the curved track?

From the problem, we get an arch A of length 5 whose endpoints are connected by a straight line B of length 4. Supposing O to be centre of curvature, we make an isocelles triangle whose equal sides are each of length l and the base is B=4. Let x (inradians) be the angle at O. So we get two unknowns : x and l (which is also radius ofcurvature). And we have two equations:

x*l=5 --->(a)

sin(x/2) = 2/l --->(b) [since we have an isocelles triangle]

solving, we get l which is required