(476) 4

Part of 1995 Tournament Of Towns

Problems(1)

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

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

Three different points

A

B

C

are placed in the plane. Construct a line

m

C

so that the product of the distances from

A

B

m

has the maximal value. Is

m

unique for every triple

A

B

C

?
(NB Vassiliev)

geometryconstructiongeometric inequality