A circle C_1 of radius 2 touches both x-axis | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the radius of circle $C_2$ be $r$. Since $C_2$ touches both axes in the first quadrant,its center is $(r, r)$.The distance from the origin $O(

Vedclass · Accepted Answer

$6 + 4 \sqrt{2}$

Vedclass · Answer

(B) Let the radius of circle $C_2$ be $r$. Since $C_2$ touches both axes in the first quadrant,its center is $(r, r)$.The distance from the origin $O(0, 0)$ to the center $A(r, r)$ is $OA = \sqrt{r^2 + r^2} = r\sqrt{2}$.The circle $C_1$ has radius $2$,so its center is $(2, 2)$. The distance from the origin to the center of $C_1$ is $OC = \sqrt{2^2 + 2^2} = 2\sqrt{2}$.Since the circles touch externally,the distance between their centers is the sum of their radii: $OA = OC + 2 + r$.Thus,$r\sqrt{2} = 2\sqrt{2} + 2 + r$.$r(\sqrt{2} - 1) = 2(\sqrt{2} + 1)$.$r = \frac{2(\sqrt{2} + 1)}{\sqrt{2} - 1} 	imes \frac{\sqrt{2} + 1}{\sqrt{2} + 1} = 2(\sqrt{2} + 1)^2 = 2(2 + 1 + 2\sqrt{2}) = 2(3 + 2\sqrt{2}) = 6 + 4\sqrt{2}$.

$A$ circle $C_1$ of radius $2$ touches both $x$-axis and $y$-axis. Another circle $C_2$ whose radius is greater than $2$ touches circle $C_1$ and both the axes. Then the radius of circle $C_2$ is-

Similar Questions

Which of the following is an amphoteric hydroxide?

Lactose is composed of .......

The angle between the lines $\vec{r}=(2 \hat{i}-3 \hat{j}+\hat{k})+\lambda(\hat{i}+4 \hat{j}+3 \hat{k})$ and $\vec{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(\hat{i}+2 \hat{j}-3 \hat{k})$ is

Epsom salt is a hydrate of which of the following?

Observe the following reaction: $2 A + B \longrightarrow C$. The rate of formation of $C$ is $2.2 \times 10^{-3} \ mol \ L^{-1} \ min^{-1}$. What is the value of $-\frac{d[A]}{dt}$ (in $mol \ L^{-1} \ min^{-1}$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module