1. **State the problem:** Find the measure of NK in a circle where one leg is 9, the hypotenuse is 15, and the other leg is unknown (NK). 2. **Formula used:** Use the Pythagorean theorem for right triangles: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse. 3. **Apply the formula:** Let $x = NK$. Then: $$9^2 + x^2 = 15^2$$ 4. **Calculate squares:** $$81 + x^2 = 225$$ 5. **Isolate $x^2$:** $$x^2 = 225 - 81$$ $$x^2 = 144$$ 6. **Take the square root:** $$x = \sqrt{144}$$ $$x = 12$$ 7. **Answer:** The measure of NK is 12.