Submitted by Elicias on Tue, 09/26/2017 - 13:10
Forums:
Hello,
I am currently working on the assignment 2 warm down, and I have found two expressions for (OX)2 in R2 and r2 but after rearranging them, I keep ending up with R2−r2=2ab−b2. 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)2and(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:
R2−a2=r2−b2R2−r2=a2−b2
The area between the two circles is π(R2−r2)=π(a2−b2)
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!