Question Number 2642 by Rasheed Soomro last updated on 24/Nov/15

n lines are drawn inside a circle in such a way that the circle has been divided in maximum number of parts. Determine this maximum number.

Commented byRasheedAhmad last updated on 24/Nov/15

•One line can divide the circle atmost 2 parts. •Two lines can divide the circle atmost 4 parts. •Three lines can divide the circle in atmost 7 parts. .... ... •n lines can divide the circle in atmost (say) m parts. ((What is m?)/)

Answered by prakash jain last updated on 24/Nov/15

n lines will divide a circle is maxium number of parts when • 3 or more lines are not concurrent • All intersection points are inside the circle Let a_i be the number of parts circle is divided into after drawing i^(th) line. a_0 =1 (no lines are drawn) a_1 =a_0 +1 a_2 =a_1 +2 a_3 =a_2 +3 a_4 =a_3 +4 ... a_n =a_(n−1) +n m=a_n =1+((n(n+1))/2)

Commented byRasheed Soomro last updated on 25/Nov/15

Excellent Sir!