Question 39

There are two concentric circles C1 and C2 with radii r1 and r2. The circles are such that C1 fully encloses C2. Then what is the radius of C1?

I. The difference of their circumference is k cm.

II. The difference of their areas is m sq. cm.


We know that r1>r2.

Statement 1: $$2\pi(r1-r2) $$ = k. We cannot determine r1 from this information

Statement 2: $$\pi(r1^2-r2^2)$$ = m. We cannot determine r1 from this information.

Using both statements together, (r1+r2)/2 = m/k. We now have two linear equations with two variables. Hence, we can determine the value of r1 in terms of m and k.

Hence, the answer can be found using both statements together.

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