MathDB

line l construction through C such that d(A,l) d(B,l) = max

Source: TOT 476 1995 Autumn S O4 - Tournament of Towns

July 9, 2024

geometryconstructiongeometric inequality

Problem Statement

Three different points

A

B

and

C

are placed in the plane. Construct a line

m

through

C

so that the product of the distances from

A

and

B

m

has the maximal value. Is

m

unique for every triple

A

B

and

C

?
(NB Vassiliev)