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Grade 12Analytical Geometry

FIVE CIRCLES C₁C₂C₃C₄AND C₅WITH RADII R₁R₂R₃R₄R₅REPECTIVELY (R₁< R₂< R₃< R₄< R₅) BE SUCH THAT C_IAND C_I+1TOUCH EACH OTHER EXTERNALLY FOR ALL I=1,2,3,4.IF ALL THE FIVE CIRCLES TOUCH EACH OF THE TWO STRAIGHT LINES L₁AND L₂ AND R₁=2 AND R₅=32 THEN R₃ IS EQUAL TO

(A) 8

(B) 17

(C) 64/17

(D) NONE OF THESE

shaurya sinha

16 Years agoGrade 12

1 Answer

Badiuddin askIITians.ismu Expert

16 Years ago

Dear shaurya sinha

circle touches next circle externally and also two lines

draw digram

you will easly get that radius of circles are in GP

given

R₁ =2 and R₅ = 32

so common ratio =2

R₃ = 2*2²

=8

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Badiuddin

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