#### Answer

The outer circle radius R = 4 in
The inner circle radius r =3 in

#### Work Step by Step

The radii of two concentric circle differ in length by exactly 1 in.
The area differ by exactly 7$\pi$ $in^{2}$
Let us assume the outer circle radius R and inner circle radius r
From the given condition R-r = 1 ..................... eq1
A1 - A2 = $\pi (R^{2} - r^{2})$
7$\pi$ = $\pi$ (R+r)(R-r)
7 = R+r .............................................eq2
Solve eq1 and eq2
R-r = 1
R+r = 7
2R = 8
R = 4 in
R-r = 1
4 -r = 1
r = 4-1 = 3in
The outer circle radius R = 4 in
The inner circle radius r =3 in