C5

Part of 2017-IMOC

Problems(1)

set closed under orthocenter

Source: IMOC 2017 C5

We say a finite set

S

|S|\ge3

is good if for any three distinct elements of

S

, they are non-collinear and the orthocenter of them is also in

S

. Find all good sets.

geometrycombinatoricscombinatorial geometry