Two concentric circles - Math Central

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Question from nazneen, a student:

select the correct answer from the given four options

given are two concentric circles. radii of outer circle & inner circle are r1 & r2 respectively.
the areas of inner circle & shaded ring are equal. the radii r1 & r2 are related by?

1. r1 = r2
2. r1 = r2*square root 2
3. r1 = r2*square root 3
4. r1 = 2r2

Hi Nazneen,

circles

The outer circle has radius $r_1 .$ What is its area?
The inner circle has radius $r_2 .$ What is its area?
What is the difference in these two areas? That is the area of the region shaded gray in my diagram.

This area is equal to the area of the inside circle. What does this tell you about $r_1$ and $r_2 ?$

Penny

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