Using Semi-circle find side of triangle The figure below above shown a bicycle path. If semicircular portion $ABC$ is $100$ $\pi$ and $CD$ is $100$$ft$ then what is $AD$? ![a busy cat\]\('\) !\two muppets I have tried to find the diamenter of the circle and the Pythagorean, I am not able figure out my answer.

The ratio of a circle's circumference to its diameter is $\pi$: $$\frac{\text{circumference}}{\text{diameter}}=\pi.$$The length of the semicircle arc is **half** the circumference of what would be the full circle. Thus, $$\frac{\text{semicircle}}{\text{diameter}}=\frac{\frac{1}{2}\cdot\text{circumference}}{\text{diameter}}=\frac{1}{2}\left(\frac{\text{circumference}}{\text{diameter}}\right)=\frac{\pi}{2}$$ Using that $\text{semicircle}=100\pi$, solve for the length of the diameter of the circle. Note that this is the same as the length of the line segment $AC$. Lastly, now apply the Pythagorean theorem.