A locomotive engine without any wagon can go at a speed of 50 km per hour and its speed diminishes by a quantity which varies as the square root of the number of wagons attached. If with 25 wagons its speed is 35 km per hour, then what is the greatest number of wagons that can be attached, if the speed is NOT to fall below 11 km per hour?
The chord of contact of tangents drawn from a point on the circle x² + y² = a² to the circle x² + y² = b² touches the circle x² + y² = c² such that b^m = a^n * c^p, where m, n, p ∈ N. Find the value of m + n + p + 10.