InterviewSolution
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InterviewSolution
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If `z_(1),z_(2),z_(3)………….z_(n)` are in `G.P` with first term as unity such that `z_(1)+z_(2)+z_(3)+…+z_(n)=0`. Now if `z_(1),z_(2),z_(3)……..z_(n)` represents the vertices of `n`-polygon, then the distance between incentre and circumcentre of the polygon isA. `0`B. `|z_(1)|`C. `2|z_(1)|`D. none of these |
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Answer» Correct Answer - A `(a)` Let vertices be `1, alpha,alpha^(2),……….,alpha^(n-1)` Given `1+alpha+alpha^(2)+…….+alpha^(n-1)=0impliesalpha^(n)-1=0` `impliesz_(1),z_(2),z_(3),……….,z_(n)` are roots of `alpha^(n)=1` which form regular polygon. So distance is zero. |
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