We know that

1 hour = 3600 seconds

1 mile = 5280 feet

So, 10 miles = 10 * 5280 = 52800 feet

Now, in 3600 seconds, man goes 52800 feet

So, in 1 second, man goes 52800/3600 feet = 44/3 feet

Hence, in 36 seconds, man travel the distance = (44/3) * 36 = 44 * 12 = 528 feet

Clearly, an arc of length 528 feet subtends 56° = 56 × π/180 radian at the center of the circular track. 

If y feet is the radius of the circular track then using the formula s = rθ we get,

      y = s/θ

=> y = 528/[56 * (π/180)]

=> y = (528 * 180 * 7)/(56 * 22) feet

=> y = 540 feet

=> y = (540/3) yards       {since, we know that 3 foot = 1 yard}

=> y = 180 yards

Therefore, the required diameter = 2 * 180 yards = 360 yards.

 Hence, the diameter of the circle is 360 yards