Let me break down the work from the image.

It appears to be a geometry or trigonometry problem involving circles and triangles. From the steps shown:

1. The setup suggests that triangle $AOB$ is formed with points $A$ and $B$ such that $\angle AOB = 90^\circ$, and the length $OA = 16 \, \text{cm}$. Additionally, a circle with center $O$ and radius $R$ is involved.

2. The equations and steps written on the page appear to solve for various values related to the geometry (like angles, radii, etc.), including using the Pythagorean theorem (as seen with the $R^2 = 100$ and $R = 10$).

It seems like the steps lead to a solution for $R = 10$, followed by solving an equation involving the values related to angles and the geometry.

Key Checkpoints:

• The equation $R^2 = 100$ is correct for the radius, as $R = 10$ is obtained.
• The use of the Pythagorean theorem for finding the length $R$ and solving the equation $\sqrt{144} = 12$ appears correct.
• The final part where you solve for $\Delta B$ using the identity $\Delta B = \theta - 0 \Delta$ (likely involving some geometric relationship) and the conclusion $x = 4$ also seems consistent.

Conclusion: It looks correct, but would you like to verify any specific step or need clarification on any part?