   SEARCH HOME Math Central Quandaries & Queries  Question from Mike, a parent: I was reviewing this question and answer: mathcentral.uregina.ca/QQ/database/QQ.02.06/phil1.html But I have trouble with this part: Now if we express the radius of the inside circle as r and the outside circle's radius is R, then this means r/R is 911/1728. But earlier we said that the outside radius R is simply w more than the inside radius r, so R = r + 282. That means that r/R = r/(r + 282). Now we can simply solve the equation for r: r/(r+282) = 911/1728 This means r = 314 mm (with rounding). Can I get more detail on the method to solve for r? Thank you, Mike Hi Mike,

From the diagrams in Stephens solution you can see that the radius R of the outside circle is the radius r of the inside circle plus w. That is

R = r + w.

Using the symmetry of a circle he also shows that r/R is 911/1728. Hence

r/(r + w) = 911/1728.

In Phil's problem w = 282 mm so

r/(r + 282) = 911/1728.

At this point multiply each side by (r + 282) to obtain

(r + 282)× r/(r + 282) = (911/1728) × (r + 282)

or

r = (911/1728) × (r + 282).

Now multiply each side by 1728 and the equation becomes

1728 × r = 911 × (r + 282).

Thus

1728 × r = 911 × r + 911 × 282

or

1728 × r - 911 × r = 911 × 282.

So

817 × r = 911 × 282

and finally

r = (911 × 282)/817 = 314 mm.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.