Darts For Beginners

Geometry Level 1

The above shows two concentric circles (circles with a common center). Given that both the area of the blue region and green region are equal, what is the ratio of perimeters between the larger circle and the smaller circle?

\sqrt2

\sqrt3

\sqrt4

\sqrt5

1 solution

Rishabh Jain
Jun 12, 2016

Relevant wiki: Circles - Area

Bigger radius $:r_1$ ; Smaller radius $:r_2$

$\large{\begin{aligned}&\pi r_2^2=\pi(r_1^2-r_2^2)\\\implies&\left( \dfrac{r_1}{r_2}\right)^2=2\\\implies& \dfrac{r_1}{r_2}=\sqrt 2\\\implies&\dfrac{2\pi r_1}{2\pi r_2}=\large\boxed{\sqrt 2}\end{aligned}}$

Darts For Beginners

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