Question

Let ABC a triangle. Take n points on the side AB, join them with C by straight lines, take n points on BC, join them with A by straight lines, take n points on AC, join them with B by straight lines. If no three straight lines meet at any point except at A,B,C then find the number of partitions in the triangle.
Please show the solution with proof

Answer 1

some sort of bug here ... i can't copy my own drawing

Answer 2

(n+1)(n+1) for two lines

Answer 3

for the third line ... each new intersection means new section ((+1 in final)

Answer 4

i cant get ur last statement

Answer 5

one intersection yields one new section ...

Answer 6

if there are n intersection (for a line) then n section + 1

Answer 7

there are 2n lines, for a single line
2n + 1 new sections,
for n line n(2n+1) new sections

Answer 8

(n+1)^2 + n(2n+1) = 3n^2 + 3n + 1

Answer 9

BRB at 20 min

Answer 10

yeah, i cant understand why 'one intersection yields one new partition' is valid.. :/

Answer 11

@FoolForMath

Answer 12

divides into two parts!! that's why each intersection yields one new section