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) & r(1)=10. The circles are such that the chord of contact of tangents from any point on C(i) to C(i+1) is a tangent to C(i+2) (i=1,2,3,....). Find the value of r(1)+r(2)+r(3)+ ......r(infinity) (where n=infinity), if the angle between the tangents from any point of C(1) to C(2) is 60.

Question

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) & r(1)=10. The circles are such that the chord of contact of tangents from any point on C(i) to C(i+1) is a tangent to C(i+2) (i=1,2,3,....). Find the value of r(1)+r(2)+r(3)+ ......r(infinity) (where n=infinity), if the angle between the tangents from any point of C(1) to C(2) is 60.

MuraliKrishna Medavaram · Answer

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