MathDB

Subset of a plane with a property

Source: Finnish Mathematics Competition 2010, Final Round, Problem 5

November 15, 2011

geometry unsolvedgeometry

Problem Statement

Let

S

be a non-empty subset of a plane. We say that the point

P

can be seen from

A

if every point from the line segment

AP

belongs to

S

. Further, the set

S

can be seen from

A

if every point of

S

can be seen from

A

. Suppose that

S

can be seen from

A

B

and

C

where

ABC

is a triangle. Prove that

S

can also be seen from any other point of the triangle

ABC