1. **Problem statement:** We have a right triangle with vertices A, 0, and B. The vertical leg from 0 to A is 33 cm, and the horizontal leg from 0 to B is the radius $r$. We want to find the length of the radius $r$. 2. **Formula used:** In a right triangle, by the Pythagorean theorem, the hypotenuse squared equals the sum of the squares of the legs: $$c^2 = a^2 + b^2$$ Here, the hypotenuse is the arc from A to B, but since the problem only gives legs, we assume the right angle is at 0, so the hypotenuse is AB. 3. **Given:** Vertical leg $= 33$ cm, horizontal leg $= r$ cm. 4. **Goal:** Find $r$ if more information is given or express the hypotenuse in terms of $r$. Since the problem does not provide the hypotenuse length or any other data, we cannot solve for $r$ numerically. However, if the hypotenuse length $c$ is known, then: $$c^2 = 33^2 + r^2$$ Rearranged to solve for $r$: $$r^2 = c^2 - 33^2$$ $$r = \sqrt{c^2 - 1089}$$ Without the hypotenuse length, the radius $r$ remains unknown. **Final answer:** The radius $r$ satisfies $$r = \sqrt{c^2 - 1089}$$ where $c$ is the hypotenuse length from A to B.