InterviewSolution
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InterviewSolution
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A circle of radius R touches externally a set of 12 circles each of radius `r` surrounding it. Each one of the smaller circles touches two circles of the set. Then `R/r=sqrtm+sqrtn-1,` where `m,n in N and m+n` is |
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Answer» Sum of interior angles of 12 sides polygon is=`(n-2)pi` `=10pi` `(10pi)/12=2(pi/2-theta/2)` `(5pi)/6=pi-theta` `theta=pi/6=30^0` `(2r)^2=R^2+R^2-2Rcostheta` `4r^2=2R(1-cos30^0)` `R^2/r^2=1/(1-sqrt3/2)` `=4/(2-sqrt3)` `=4(2+sqrt3)` `R/r=sqrt2*sqrt(4+2sqrt3` `=sqrt2*(sqrt3+1)` `=sqrt6+sqrt2` m=6,n=2 m+n=6. |
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