Submitted by Elicias on Tue, 09/26/2017 - 13:10

Hello,

I am currently working on the assignment 2 warm down, and I have found two expressions for $(OX)^2$ in $R^2$ and $r^2$ but after rearranging them, I keep ending up with $R^2 - r^2 = 2ab-b^2$. I know that I have clearly done something wrong algebraically or else I have misinterpreted the lengths of the sides involved.

I would appreciate any pointers on where my mistake could be.

Thank you for your help!

p.s. I hope the maths formatting works!

## The maths formatting looks

The maths formatting looks great!

Assuming that $X$ is the point where the radius meets the line AB we have:

\[

(OX)^2 = (OB)^2 - (XB)^2 \quad \text{and} \quad (OX)^2=(OP)^2 - (XP)^2

\]

From the information in the question we have $OB=R$, $XB=a$, $OP=r$, $XP=b$. Using this

and equating the expressions for $(OX)^2$ gives us:

\[

R^2-a^2=r^2-b^2\\

R^2-r^2=a^2-b^2

\]

The area between the two circles is $\pi (R^2-r^2)=\pi(a^2-b^2)$

## I think you had $PB=b$ rather

I think you had $PB=b$ rather than $XP=b$?

## Aha!

Yes, that would make a lot of sense, it seem I had misread the question.

Thank you for your help!