A circle has a radius of three inches. The distance from the center of the circle to chord $CD$ is two inches. How many inches long is chord $CD$? Express your answer in simplest radical form.
Let's label the center of the circle as point $A$. That's a good idea. What's the relationship between $r$ and $d$? We can use the Pythagorean Theorem because we have a right triangle. Right. Our goal is to find $CD$. So let's rearrange the equation to solve for it. That gives $CD = 2\sqrt{r^2 - d^2}$. And we know that $r$ is three inches and $d$ is two inches. That means that $CD = 2\sqrt{3^2 - 2^2} = 2\sqrt{5} = 2\sqrt{5}$ inches. Right. $CD = 2\sqrt{5}$ inches.

