If radii of the smallest and largest circle passing through the point -3-2 and touching the circle x2 - y62 - 2 -2y - 2 -0 are r1 and r2 respectively- then the mean of r1 and r2 is

REF.Imagecentre of given circle = (0, √(2)) radius given circle, r=√(0+2+2)=2 oo^1=√(3)⇒ r+r_1=√(3) r_1+r+r=r_2⇒√(3)+2=r_2 ⇒ r_1=√(3) 2 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Physics

Pascal's Law

If radii of t...

Question

If radii of the smallest and largest circle passing through the point $(\sqrt{3}, \sqrt{2})$ and touching the circle
$x^{2} + y 62 - 2 \sqrt{2} y - 2 = 0$ are $r_{1}$ and $r_{2}$ respectively, then the mean of $r_{1}$ and $r_{2}$ is

Open in App

Solution

REF.Image
centre of given circle = $(0, - \sqrt{2})$
radius given circle, $r = \sqrt{0 + 2 + 2} = 2$
$o o^{1} = \sqrt{3} \Rightarrow r + r_{1} = \sqrt{3}$
$r_{1} + r + r = r_{2} \Rightarrow \sqrt{3} + 2 = r_{2}$
$\Rightarrow r_{1} = \sqrt{3} - 2$
Mean $\Rightarrow \frac{r_{1} + r_{2}}{2} = \frac{2 \sqrt{3}}{2} = \sqrt{3}$

Suggest Corrections

Similar questions

Q. Find radii of smallest and largest circle passing through the point

(\sqrt{3}, \sqrt{2})

and touching the circle

x^{2} + y^{2} - 2 \sqrt{2} y - 2 = 0 a r e r_{1} a n d r_{_{2}}

respectively.

Q. Let

r_{1}

and

r_{2}

be the radii of the largest and smallest circles, respectively, which pass through the point

(- 4, 1)

and having their centres on the circumference of the circle

x^{2} + y^{2} + 2 x + 4 y - 4 = 0.

\frac{r_{1}}{r_{2}} = a + b \sqrt{2,}

then

a + b

is equal to:

Q. Let

r_{1}

and

r_{2}

represent the radii of the smallest and largest circles passing through

(a, \frac{1}{a})

and touching the circle

4 x^{2} + 4 y^{2} - 4 x - 8 y - 31 = 0

, where

a

is the least possible value of ratio of the sides of the regular

n

sided

(n \geq 3)

polygons inscribed and circumscribed to a unit circle, then

r_{1} + r_{2}

Q. Three circles

C_{1}, C_{2}

and

C_{3}

with radii

r_{1}, r_{2}

and

r_{1} + r_{2}

respectively are such that

C_{1}

and

C_{2}

touch each other externally and

C_{3}

internally. Another circle with radius

r_{3}

touches all the three circles. If

r_{1} > r_{2} > r_{3}

and

r_{1}, r_{2}, r_{3}

are in A.P. then

{(\frac{r_{1}}{r_{2}})}^{3}

A

: lf the circles

x^{2} + y^{2} = a^{2},

x^{2} + y^{2} - 6 x - 8 y + 9 = 0

touch externally then

a = 1

R

: Two circles with centres

C_{1}, C_{2}

and radii

r_{1}, r_{2}

respectively touch externally iff

C_{1} C_{2} = r_{1} + r_{2}

Join BYJU'S Learning Program

If radii of the smallest and largest circle passing through the point (√3,√2) and touching the circle x2+y62−2√2y−2=0 are r1 and r2 respectively, then the mean of r1 and r2 is

REF.Imagecentre of given circle = (0,−√2)radius given circle, r=√0+2+2=2oo1=√3⇒r+r1=√3r1+r+r=r2⇒√3+2=r2⇒r1=√3−2Mean ⇒r1+r22=2√32=√3

If radii of the smallest and largest circle passing through the point $(\sqrt{3}, \sqrt{2})$ and touching the circle
$x^{2} + y 62 - 2 \sqrt{2} y - 2 = 0$ are $r_{1}$ and $r_{2}$ respectively, then the mean of $r_{1}$ and $r_{2}$ is