MathDB

A circle

\mathcal C

and five distinct points

M_1,M_2,M_3,M_4

and

M

\mathcal C

are given in the plane. Prove that the product of the distances from

M

to lines

M_1M_2

and

M_3M_4

is equal to the product of the distances from

M

to the lines

M_1M_3

and

M_2M_4

. What can one deduce for

2n+1

distinct points

M_1,\ldots,M_{2n},M

\mathcal C

Problem Statement