word problem with factoring?

Question

"A track runs along the outer edge of a circular park. The track is the same width all the way around the park. The area inside the track is given by the trinomial (pi)r^2 - 4(pi)r+4(pi), where r is the radius of the entire park in meters."

1. Factor (pi)r^2 - 4(pi)r+4(pi) completely:
2. What is the width of the track?
3. If the entire area of the park inside the track is 100(pi), what is the radius of the entire park?

Answer 1

well it factors nicely to
(pi)(r-2)(r-2)

2. notice how that factorization looks very like pi r^2. if the area of the circular park is given by that equation, and r is the entire park including the track, then intuitively the difference between 'r' and inner radius that doesn't include the track must be the '-2' in the factor.
so the width is 2 meters

3. well if the park is (pi)100, and the area is pi(r^2) then r of the park must be 10. and if the width is 2, then the radius of the entire park is 12.