3

Part of 1928 Eotvos Mathematical Competition

Problems(1)

min of longer of lengths AP,BP

Source: Eotvos 1928 p3

\ell

be a given line,

A

B

given points of the plane. Choose a point

P

\ell

so that the longer of the segments

AP

BP

is as short as possible. (If

AP = BP,

either segment may be taken as the longer one.)

geometryGeometric Inequalitiesconstruction