Question

If AB=7, what is the area between the two circles?

Answer 1

Suppose the two circles are concentric.
CB = 7/2 = 3.5 (line joining from centre perpendicular to chord bisects chord)
By Pyth. Thm.,
\[r_2^2 = r_1^2 + 3.5^2\]So, \[r_2^2 - r_1^2 = 3.5^5\]

Area between two circles
= area of big circle - area of small circle
\[= \pi (r_2^2 - r_1^2)\]The rest are substitution and calculations.

Answer 2

*facepalm*
For the sixth line, it should be
\[r_2^2 - r_1^2 = 3.5^2\]