VTMO 2014 — Grade 9 — semifinal Question 20

Question 20

Circles $\left(A\right) , \left(B\right)$ touch both sides of the right angle xOy. Center $A$ lies on circle $\left(B\right)$, whose circle is larger as pictured. Find rB/rA.

Question illustration

$2 - \sqrt{2}$
$\sqrt{2} - 1$
$\frac{1}{\sqrt{2} - 1}$
$\frac{1}{\sqrt{2} + 1}$
$2 + \sqrt{2}$