# Thread: Writing a formula from a circle and triangle

1. ## Writing a formula from a circle and triangle

I need help with part a. I don't understand how to write the formula. Please explain and show to me step by step on how to do this problem. Thanks.

2. To find $\displaystyle d$ you can use pythagorus' theorem. The hypotenuse is $\displaystyle x+r$, and the other side is $\displaystyle r$. Then note that $\displaystyle \theta=tan^{-1}\left ( \frac{d}{r} \right )$.

3. What about theta in that formula? How would I find out what that is in order to find d?

4. It's asking for $\displaystyle d$ in terms of $\displaystyle x$ and $\displaystyle r$. You don't need theta for this part of the question:

$\displaystyle d=\sqrt{(x+r)^2-r^2}$

You can simplify this formula.