1. The problem asks to find the value of angle $B$ in the context of a square ABCD with side length 22 cm and an inscribed circle. 2. Since ABCD is a square, all its interior angles are right angles. 3. Therefore, angle $B$ is one of the interior angles of the square. 4. By definition, each interior angle of a square measures $90^\circ$ or $\frac{\pi}{2}$ radians. 5. Hence, angle $B = \frac{\pi}{2}$ radians. Final answer: $\boxed{\frac{\pi}{2}}$ radians.