Home
Class 11
MATHS
Let nge3 and let C(1),C(2),....,C(n) be...

Let `nge3` and let `C_(1),C_(2),....,C_(n)` be circles witht radii, `r_(1),.r_(2),....,r_(n),` respectively. Assume that `C_(1) and C_(i+1)` touch external for `2leilen-1`. It is also given that the x-axis and the line `y=2sqrt(2)x+10` are tangential to each of the ci rcles. Then `r_(1),r_(2),....,r_(n),` are in-

A

An arithmetic progression with common difference `3 + sqrt2`

B

A geometric progression with common ratio `3 + sqrt2`

C

A arithmetic progression with common difference `2 + sqrt3`

D

A geometric progression with common ratio `2 + sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Similar Questions

Explore conceptually related problems

Let nge3 and let C_1, C_2, ...., C_n, be circles with radii r_1, r_2,... r_n, respectively. Assume that C_i and C_(i+1) touch externally for 1leilen-1. It is also given that the x-axis and the line y = 2sqrt(2)x+10 are tangential to each of the circle . Then r_1,r_2.r_n are in (A) an arithmetic progression with common difference 3+sqrt(2) (B) a geometric progression with common ratio 3+sqrt(2) (C) an arithmetic progression with common difference 2+sqrt(3) (D) a geometric progression with common ratio 2+sqrt(3)

Three circles with centres C_(1),C_(2) and C_(3) and radii r_(1),r_(2) and r_(3) where *r_(-)1

Consider a series of 'n' concentric circles C_1, C_2, C_3, ....., C_n with radii r_1, r_2, r_3, ......,r_n respectively, satisfying r_1 > r_2 > r_3.... > r_n and r_1= 10. The circles are such that the chord of contact of tangents from any point on C_1 to C_(i+1) is a tangent to C_(i+2) (i = 1, 2, 3,...). Find the value of lim_(n->oo) sum_(i=1)^n r_1, if the angle between the tangents from any point of C_1 to C_2 is pi/3.

Three circles C_(1),C_(2),C_(3) with radii r_(1),r_(2),r_(3)(r_(1)ltr_(2)ltr_(3)) respectively are given as r_(1)=2 , and r_(3)=8 they are placed such that C_(2) lines to the right of C_(1) and touches it externally C_(3) lies ot the right of C_(2) and touches it externally. There exist two stratight lines each of whic is a direct common tangent simultaneously to all the three circles then r_(2) is equal to

Circles C_(1) and C_(2) of radii r and R respectively, touch each other as shown in the figure. The lime l, which is parallel to the line joining the centres of C_(2) and C_(2) is tangent to C_(1) at P and intersects C_(2) at A,B.If R^(2)=2r^(2) , then angleAOB equals-

C_1 and C_2 are fixed circles of radii r_1 and r_2 touches each other externally. Circle 'C' touches both Circles C_1 and C_2 extemelly. If r_1/r_2=3/2 then the eccentricity of the locus of centre of circles C is

Two circles of radii r_(1) and r_(2)(r_(1)>r_(2)) touch each other exterally.Then the radius of circle which touches both of them externally and also their direct common tangent is (A) ( sqrtr_(1)+sqrt(r)_(2))^(2) (B) sqrt(r_(1)r_(2))(C)(r_(1)+r_(2))/(2) (D) (r_(1)-r_(2))/(2)

Prove that C(n,r)+C(n-1,r)+C(n-2,r)+......+C(r,r)=C(n+1,r+1)

Given that C(n, r) : C(n,r + 1) = 1 : 2 and C(n,r + 1) : C(n,r + 2) = 2 : 3 . What is r equal to ?

Given that C(n, r) : C(n,r + 1) = 1 : 2 and C(n,r + 1) : C(n,r + 2) = 2 : 3 . What is n equal to ?