Question

The number of parts into which a plane is divided by $10$ distinct straight lines drawn in the plane passing through a single point is

• A. $18$
• B. $38$
• C. $25$
• D. $20$

Answer 1

The correct option is D $20$

The maximal number of regions into which n lines divide a plane is

$N\left(n\right)=\frac{1}{2(n^2+n+2)}$

which, for $n=1,2,...$ gives $2,4,7,11,16,22,$ the same maximal number of regions into which a circle, square, etc. can be divided by n lines.

The number of parts into which a plane is divided by 10 distinct straight lines drawn in the plane passing through a single point is $20$