10 Lines in a Plane: Word Problem

Question

There are 10 lines in a plane, each of which intersects all the others and no three of these lines are concurrent.

a) Into how many regions do the lines divide the plane?

b) How many points of intersection are there?

Answer 1

L_n represents the number of regions created by n intersecting lines.

L_n = (n² + n + 2) / 2

How many regions do 10 lines create?

(Proofs are on line, e.g., "www.cut-the-knot.org/proofs/LinesDividePlane/shtml)