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Putnam 1947 A3

Source: Putnam 1947

April 3, 2022

Putnamgeometrypolygonlines

Problem Statement

Given a triangle

ABC

with an interior point

P

and points

Q_1 , Q_2

not lying on any of the segments

AB , AC ,BC,

AP ,BP ,CP,

show that there does not exist a polygonal line

K

joining

Q_1

and

Q_2

such that i)

K

crosses each segment exactly once, ii)

K

does not intersect itself iii)

K

does not pass through

A, B , C

or

P.

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