Question
$${C_1}$$ is a circle of radius 1 touching the $$x$$-axis and the $$y$$-axis. $${C_2}$$ is another circle of radius $$> 1$$ and touching the axes as well as the circle $${C_1}.$$ Then the radius of $${C_2}$$ is :
A.
$$3 - 2\sqrt 2 $$
B.
$$3 + 2\sqrt 2 $$
C.
$$3 + 2\sqrt 3 $$
D.
none of these
Answer :
$$3 + 2\sqrt 2 $$
Solution :
Clearly from the figure,
$$\eqalign{ & \frac{r}{{\sqrt 2 + 1 + r}} = \sin \,{45^ \circ } \cr & \Rightarrow r = 3 + 2\sqrt 2 \cr} $$
Clearly from the figure,
$$\eqalign{ & \frac{r}{{\sqrt 2 + 1 + r}} = \sin \,{45^ \circ } \cr & \Rightarrow r = 3 + 2\sqrt 2 \cr} $$