MathDB

Three parallel lines

\ell_1, \ell_2

and

\ell_3

of a plane are given such that the line

\ell_2

has the same distance

a

from

\ell_1

and

\ell_3

. We put

5

points

M_1, M_2, M_3,M_4

and

M_5

on the lines

\ell_1, \ell_2

and

\ell_3

in such a way that each line contains at least one point. Detennine the maximal number of isosceles triangles that are possible to be formed with vertices three of the points

M_1, M_2, M_3, M_4

and

M_5

in the following cases: (i)

M_1,M_2,M_3 \in \ell_2, M_4 \in \ell_1

and

M_5 \in \ell_3

. (ii)

M_1,M_2 \in \ell_1, M_3,M_4 \in \ell_3

and

M_5 \in \ell_2

Problem Statement