Mathematics

Problem

Let A, B and C be three non-collinear points. Line

\ell_1

is the unique line through A and B, and line

\ell_2

is the unique line through B and C. If a point D lies on both

\ell_1

and

\ell_2

, which of the following must be true? a)

D

coincides with

A

D

is different from

A,\,B

and

C

D

coincides with

B

D

is the midpoint of

\overline{AB}