1. **Problem:** How do you find the radius of a circle, and can you show an example? 2. **Formula:** The radius is half of the diameter. $$r=\frac{d}{2}$$ If you know the circumference, you can also use: $$C=2\pi r$$ 3. **Important rule:** - If the diameter is given, divide by $2$. - If the circumference is given, divide by $2\pi$. - The radius is always the distance from the center to the circle. 4. **Example using the diameter:** Suppose the diameter is $10$. $$r=\frac{d}{2}=\frac{10}{2}$$ $$r=5$$ So the radius is $5$. 5. **Example using the circumference:** Suppose the circumference is $31.4$. $$C=2\pi r$$ $$31.4=2\pi r$$ Divide both sides by $2\pi$: $$\frac{31.4}{2\pi}=\frac{2\pi r}{2\pi}$$ $$\frac{31.4}{2\pi}=r$$ $$r\approx 5$$ 6. **Final answer:** The radius is found by dividing the diameter by $2$, or by using $r=\frac{C}{2\pi}$ if the circumference is known. In the example, the radius is $5$.